Papers

Many multivariate extremes models have intractable likelihoods requiring practitioners to use alternative fitting methods. The tail pairwise dependence is a summary measure of the dependence in the tail of any multivariate regular variation model. We develop an objective function for model fitting that relies on the tail pairwise dependence as the link between our desired model (that does not have a likelihood) and a proxy model (that has a likelihood). We employ the bivariate Hüsler-Reiss distribution as the proxy model and show that there is a one-to-one relationship between the dependence parameter and the tail pairwise dependence value. Our proxy-likelihood estimator is fully developed for the transformed linear extremes time series (TLETS) models of Mhatre and Cooley (2024) and is applied to the wildfire weather data of Wixson and Cooley (2023). Simulations demonstrate that the proxy-likelihood is a competitive TPD estimator, is better at fitting TLETS models than existing methods, and is amenable to likelihood-based model selection techniques. Our estimator has smaller bias when tail dependence is weak than existing estimators reducing the need for bias adjustments. Without these adjustments, we note an increase in the tail dependence in weather-related wildfire risk between past and present climates.

Variable selection using information criteria has an explicit statistical target but requires discrete search over candidate models. The smooth information criterion (SIC) replaces the discontinuous model-dimension term by a differentiable approximation, with an $\epsilon$-telescoping continuation strategy progressively sharpening this approximation without data-driven selection of a regularisation-strength parameter. We develop SIC as a general procedure for coefficient-level variable selection in generalised linear models (GLMs) and use it to address a central question: how faithfully does smooth optimisation reproduce the corresponding discrete information-criterion selection problem? Focusing on BIC, we benchmark SIC directly against exhaustive subset selection where feasible, using exact support agreement, BIC difference and selection behaviour across a varying signal-strength boundary. Simulations in Gaussian, binomial and Poisson regression show that SIC closely reproduces exhaustive BIC selection and tracks the exact BIC selection boundary. Relative to stepwise BIC, LASSO, SCAD and MCP, SIC produces competitive variable-selection performance while retaining sparse models, with predictive performance broadly comparable across methods. Computational advantages over stepwise BIC increase with predictor dimension. In a real-data application with 16 candidate predictors, SIC recovers the globally BIC-optimal model among all 65,536 supports at a small fraction of the computational cost of exhaustive enumeration.

This paper introduces a novel semiparametric testing framework for localized point-impact effects within a spatial semi-functional linear regression model. We address an intricate inferential problem that simultaneously accommodates three distinct sources of complexity: an infinite-dimensional global functional slope, an unknown smooth spatial nuisance surface, and data-dependent, unobserved impact locations. To isolate the point-impact coefficients, we construct a robust residualized cross-moment estimator after regularizing the functional component via Tikhonov inverse and estimating the spatial nuisance surface through local-linear smoothing. We establish a multivariate central limit theorem under the null hypothesis of no point-impact effect. We develop two operational test statistics: a general formulation whitened by the long-run covariance matrix to handle arbitrary spatial dependence, and a simpler chi-square calibration valid under short-range spatial dependencies in regression errors. Rigorous finite-sample simulations and an application to Canadian weather data demonstrate the superior power and size control of our methodology.

Early-phase dose-finding methods increasingly assess toxicity and efficacy jointly, but comparisons based only on administered dose may inadequately characterize regimens differing in schedule. We developed a Bayesian phase II adaptive platform design for regimen optimization that integrates pharmacokinetic/pharmacodynamic (PK/PD) modelling into toxicity, efficacy, regimen selection and adaptation decisions. The proposed PK/PD-informed Regimen Optimization Platform (PROP) design uses a population PK/PD model to generate patient- and population-level predictions of exposure and biological activity. Acute and cumulative toxicities are analysed using a discrete-time time-to-event model informed by PK exposure. Efficacy is evaluated through Bayesian model averaging of exposure-driven and biomarker-driven time-to-event models. The design supports regimen graduation, discontinuation for futility or safety, and addition of unexplored regimens. Performance was evaluated through simulations motivated by an influenza intensive-care setting. Across six scenarios, PROP generally improved graduation and futility decisions, reduced inappropriate graduation, and supported the addition of promising regimens compared with dose-based alternatives. It also more accurately estimated regimen-specific toxicity and arm-specific efficacy, while the model-averaging framework favored the efficacy model consistent with the data-generating mechanism. Dose-based approaches performed better for safety stopping in some scenarios, despite less accurate characterization of the regimen–toxicity relationship. PK/PD-informed platform designs can improve adaptive regimen selection and knowledge generation when dose alone cannot adequately characterize treatment regimens.

Thin plate splines are highly attractive smoothers. However, they have cubic computational cost, which severely limits their use in practice. As a remedy, Wood (2003) suggested thin plate regression splines (TPRS), which provide a low rank approximation. The key step of the TPRS approximation is a truncated eigendecomposition of the radial basis function (RBF) design matrix. However, as Wood (2003) writes, the optimality of the TPRS approximation is a slightly weak one. This is because the RBF coefficients are subject to orthogonality constraints and the TPRS approximation is only optimal if these constraints are ignored. To address this shortcoming, we suggest a slightly different low rank approximation. The suggested approximation is based on a truncated Demmler-Reinsch basis (TDRB), which provides a best low rank approximation of the smoother matrix in terms of Frobenius and spectral norm. We prove that the TDRB smoother achieves the optimal rate of convergence and suggest an efficient algorithm for its construction. This algorithm is based on a truncated Karhunen-Loève (KL) expansion of the equivalent Bayesian smoothness prior and it has the same computational cost as required for TPRS. We demonstrate the applicabilty of our approach through simulations and a real data example. We find that the performance is very similar to that of TPRS but the suggested approach has some advantages.

Under Gaussian sampling, removing location and scale turns the sample into a direction that is uniformly distributed on a sphere of dimension $n-2$, and sample skewness and kurtosis become a cubic-quartic polynomial image of spherical measure. We use this geometry to obtain exact finite-sample results for the Jarque-Bera statistic $\mathrm{JB}_n$. First, for every $n\ge 3$ the largest attainable value of $\mathrm{JB}_n$ is $n\{(n-2)^4+4(n-1)^2\}/\{24(n-1)^2\}$, attained by a single-outlier sample, so the asymptotic $10\%$ and $5\%$ tests have size zero for $n\le 6$ and the $1\%$ test for $n\le 7$; near this maximum the density of $\mathrm{JB}_n$ behaves like an explicit multiple of $(J_n^+-x)^{(n-4)/2}$. Second, passing from residual coordinates to power sums writes the joint density of skewness and kurtosis as an integral of the reciprocal square root of a polynomial discriminant; for every $n\ge 5$ the innermost integral runs over a single interval and is a Lauricella $F_D$ period. Third, this yields explicit laws: an arcsine law for $n=3$, an algebraic joint density for $n=4$, and a single complete elliptic integral, equivalently ${}_2F_1(\tfrac12,\tfrac12;1;\cdot)$, for $n=5$. Residual-coordinate collisions generate the discriminant singularities of the joint law, while stationary points of $\mathrm{JB}_n$ on the residual sphere govern the singularities of its one-dimensional density.

Consider an optimal dynamic treatment regime, $g^{\textbf{opt}}$ correctly identified from a large, perfectly executed sequentially randomized experiment. Even when the experimental results are generalizable to a future target population, there is no guarantee that $g^{\textbf{opt}}$ outperforms human decision-makers; human experts can do better than $g^{\textbf{opt}}$ whenever they have access to relevant information beyond the covariates recorded in the experiment. Motivated by this observation, we derive results on a new class of regimes called initiation regimes, which generalize existing results on superoptimal regimes. These regimes follow human decision-makers up to the point where it becomes more beneficial to initiate a sequential optimal regime, and are guaranteed to outperform both purely human and purely algorithmic decision rules, e.g., based on reinforcement learning algorithms. Furthermore, we present modified experimental designs that identify the best initiation regimes, show how the best initiation regime can be identified from classical observational data under explicit assumptions, and give estimation and statistical inference methodology for these regimes. To illustrate the practical utility of the methods, we consider initiation regimes in a case study on treatment of lower back pain.

Adaptive algorithms increasingly make decisions while reshaping the dynamics that generate their future data. We establish a shrinking-tube concentration bound for projected stochastic approximation driven by an adaptive Markov chain. The bound guarantees, with high probability, that every iterate after a chosen time remains within a tolerance around the target that tightens over time. The probability of any exit after the chosen time admits a polynomially decaying upper bound, and a matching lower bound shows that its polynomial exponent cannot be improved in general under finite second moments. The result therefore identifies a sharp tradeoff between how quickly the tolerance shrinks and how rapidly the probability of any future exit decreases. We also extend the analysis to recursions with additional martingale-difference noise and predictable bias, showing how growth in the martingale-difference noise scale slows the decay of the exit-probability bound while predictable bias restricts the admissible tube shrinkage. The proof combines backward kernel replacement, a finite-time mean-squared-error bound, and a blockwise maximal first-exit argument. We apply the theory to inventory learning with stockout-dependent demand and fixed stockout costs, and quantify how numerical gradient accuracy affects the all-future reliability of the resulting policies.

Traditional multivariate copulas often fail to capture complex dependence structures and may impose restrictive assumptions that limit their applicability to real-world data. To address these issues, vine copulas provide a flexible framework by constructing multivariate models from bivariate copulas. The three main types are D-vines, C-vines and R-vines. To simplify computations, the simplifying assumption is often applied, assuming conditional copulas are independent of conditioning variables. This results in some variables exerting minimal influence on the conditional copulas. Therefore, this study explores two subclasses of R-vines with node degrees capped at three, assessing its performance against existing models. The statistical results demonstrate that the proposed degree-constrained vine structures can serve as effective alternatives to existing vine copula models.

In genomics, imaging and clinical studies, only a few of many candidate predictors are often nonlinearly associated with a response that may be, e.g. binary, categorical, a count or a censored event time. The Terminating-Random Experiments (T-Rex) selector is a scalable variable selection method that controls the false discovery rate (FDR) by letting synthetic null variables (dummies) compete with the real predictors. While the FDR control theory embraces more general settings, to date, the T-Rex selector has been specified only for linear models. We propose a memory-efficient selection procedure with FDR control for generalized linear models and Cox regression by extending the recently developed virtual dummy construction to score-based forward selection for Bernoulli, Poisson, multinomial and Cox responses. The virtual-dummy-based selection path remains equal in distribution to explicit augmentation, so FDR control carries over under the same assumptions. Simulations confirm this equivalence and the power gained by correct model specification. Real-world applicability is illustrated on simulated genotypes and on cancer survival data.

Gaussian processes (GPs) provide a flexible nonparametric framework for modeling time series through appropriately chosen kernel functions. This chapter introduces the basic formulation of Gaussian processes, commonly used kernels, GP regression, hyperparameter estimation, and model evaluation using in-sample and out-of-sample criteria. Applications to stationary, quasi-periodic, and seasonal time series illustrate how individual and composite kernels can represent different forms of temporal variation. Additive kernels also provide interpretable decompositions into latent components such as trend, smooth local variation, and seasonality, while product kernels allow more complex dependence structures to be constructed. Finally, Gaussian process state-space models (GP-SSMs) are briefly introduced, and a nonlinear example demonstrates how a GP transition model can be combined with particle filtering and smoothing for latent-state estimation.

We propose Sufficiently Reduced Distributional Regression (SRDR), a generative method that combines conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). It builds on a characterization of sufficiency through strictly proper scoring rules: a dimension reduction is sufficient if and only if predicting the response from the reduced covariates incurs no loss in expected score relative to the full covariates. Sufficient dimension reduction thus becomes a risk minimization problem. SRDR jointly trains a dimension reduction map and a generative prediction model by minimizing the energy score, which can be estimated by sampling without density evaluation or adversarial training. The framework extends to multi-environment data and to classification. We prove that the estimated conditional distributions converge in energy distance to the true ones, which implies that the learned representation is asymptotically sufficient. In simulations and applications to CT slice localization, superconductivity, and digit classification, SRDR recovers low-dimensional sufficient structure and matches or outperforms state-of-the-art nonlinear SDR methods in representation quality and predictive performance.

The coalescent is a central framework in population genetics for modelling the ancestral relationships among sampled individuals through a genealogy, represented as a rooted and ranked binary tree. In this model, lineages coalesce at a rate inversely proportional to the effective population size, a time-varying quantity of primary interest. The bounded coalescent conditions genealogies on the time to the most recent common ancestor being bounded above by a fixed time. This model is useful in various contexts, such as phylodynamics of infectious diseases with known introduction times and single-cell lineage tracing in synthetic barcoding experiments. To our knowledge, there is no existing tool that infers variable effective population size trajectories under the bounded coalescent. We view estimation under the bounded coalescent as equivalent to estimation of the intensity function of an inhomogeneous point process. We provide an efficient algorithm for coalescent simulation under the bounded coalescent using point process methods, retaining the exactness of naive rejection sampling while substantially reducing computational cost and avoiding repeated numerical inversion of the bounded cumulative hazard. We then develop a Markov chain Monte Carlo procedure for posterior inference of effective population size trajectories that avoids discretization of the likelihood integrals. In simulations, conditioning on the bound reduces the median sum of squared errors in two of three settings, with less favourable results in the most rapidly varying setting. We illustrate the method using severe acute respiratory syndrome coronavirus 2 sequence data from Washington State.

Covariates summarized over a subject's completed follow-up are sometimes entered into Cox regression as though observed at baseline. This practice incorporates future event or censoring information and changes both the estimand and its sampling behavior. We analyze an affine class in which a genuine baseline covariate is contaminated by realized follow-up time. Treating partial likelihood as an observed-data estimation criterion, we derive the population score and characterize its unique least-false coefficient. Exact continuous-time benchmarks show scale reduction and saturation under strong contamination, while administrative censoring destroys the reduction and may produce overshoot. Grouping exit times with Breslow ties changes the geometry: the coefficient has a single hump and eventually returns to zero even though the induced association diverges. We also derive an observed-data influence function and show why model-based variance can be either too small or too large. A subject-level sandwich consistently estimates uncertainty around the least-false target under the stated conditions, but it does not correct the target itself.

Panel conditioning, the causal effect of prior survey participation on responses, can vary with tenure. Under an additive model of cell means in period, entry cohort, and tenure, we characterize which features of the conditioning path a staggered panel identifies on its observed support, and how the unidentified component affects common panel estimators. The identified set of the path is an affine translate of the tenure projection of the cell design's kernel, and a linear functional of the path is identified exactly when it annihilates that projection. It always contains an affine direction and, when the entry cohorts share a stride, periodic directions, which exhaust it under a connectivity condition on observed increments; second differences at that stride are then identified, and ordinary ones generally are not when the stride exceeds one. Under a recruitment condition, an interrupted schedule such as the four-eight-four rotation of the Current Population Survey (CPS) distinguishes a constant increment per interview from one per calendar month, which no equally spaced schedule can. We give support conditions for recovery under a plateau, entry-wave negative controls, or bounded cohort drift. A second set of results links identification to regression: two-way fixed effects absorb every unidentified direction, so the remaining conditioning bias is normalization-invariant and itself identified, and a two-way regression with tenure indicators corrects it under a residual-rank condition. When event time is aligned with tenure, conditioning shifts event-study coefficients by a known linear functional of the path, producing pre-trends without anticipation; bounds on identified curvature bound those shifts. Simulations verify the identities, a 19-wave Japanese panel illustrates the support calculations, and published CPS month-in-sample indices give a descriptive, not identifying, example.

Competing-risks data do not identify latent marginal duration distributions or their dependence without additional restrictions. This paper asks whether restrictions introduced to restore identification themselves restrict the observable law. For a two-risk Archimedean model with categorical exclusion restrictions, we derive a necessary-and-sufficient observable characterization. A discrete single-crossing argument identifies the scalar copula parameter from cell-specific overall survival probabilities, while cause indicators recover the remaining allocation and generate additional specification restrictions. We construct an identification-robust, self-normalized quadratic statistic, invert it to obtain confidence sets, and use empty inverted sets as a conservative specification test. Simulations show that the cause indicator can be decisive: under the weakest contrast considered it converts a frequently uninformative survival-based confidence set into an informative joint set without loss of coverage, whereas excessive categorical contrast can eliminate causes from individual cells and make cause-specific recovery inadmissible. The results turn latent exclusion restrictions into refutable restrictions without estimating covariate derivatives.

Large language models are increasingly used as inexpensive judges to evaluate outputs, label data, and assess whether a system meets a desired quality standard. Yet using AI judgments for formal statistical inference is fundamentally different from simply treating them as ground-truth labels: AI evaluations can be biased or noisy, and rigorous hypothesis testing requires explicit control of type-I and type-II errors. We study how to use AI judgments, together with selective human verification, to conduct a valid hypothesis test at minimum cost. We consider a population of items with hidden binary labels. After choosing a fixed pool of items, the decision maker can selectively query AI, send an item directly to a human, escalate an AI-scored item to a human after observing the AI report, or stop once sufficient evidence has accumulated. We derive an information-theoretic lower bound that captures the minimum cost of achieving prescribed testing errors and characterizes the value of AI information and human verification through a report-dependent information frontier. Motivated by this characterization, we develop SCALE, a sequential cost-aware policy that combines selective AI scoring with adaptive human escalation. SCALE is valid at finite sample sizes and matches the lower bound to first order as the target error probabilities vanish. We further extend the framework to an unknown AI-output model using paired AI-human pilot data. Numerically, SCALE approaches Human-only or AI-only testing when one source clearly dominates, while achieving its largest savings when inexpensive AI judgments and selective human verification are both valuable.

Causal discovery from observational and interventional data becomes challenging in the presence of latent confounding and selection bias, where causal structure is no longer adequately represented by directed acyclic graphs over observed variables. Existing model-free methods often rely on an exponential number of conditional independence tests and provide limited uncertainty quantification in high-dimensional settings. We develop a model-free and constraint-query optimal statistical inference framework for causal discovery under latent variables and selection using single-target interventions. We introduce the system-induced subgraph (SIS) to capture the causal relations among system variables while accounting for context variables. We establish its identifiability through maximal ancestral graphs (MAGs), and show that interventions on each observed system variable are sufficient for unique identification and necessary in the worst case. Building on these results, we develop a two-stage graph inference procedure with asymptotic family-wise error control under sufficient first-stage power. For $d_X$ observed system variables, the procedure requires at most $\frac{5}{2}d_X^2$ statistical tests, parallelizable within each stage, and achieves optimal constraint-query complexity up to a constant factor. The framework accommodates soft interventions and avoids parametric structural equation assumptions. We illustrate the methods through analysis of Perturb-seq data from interferon-$\beta$-stimulated A549 lung cancer cell lines.

Matrix time series is a series of matrix data observed over time. Analytical tools for such time series is needed in many applications in finance, economics, engineering and many other fields. To avoid the use of vectorization of the matrices which loses the column and row information, and the vector autoregression framework in traditional time series analysis, \cite{chen2021autoregressive} proposed the Matrix Autoregressive (MAR) Model. The model maintains and utilizes the matrix structure, leading to a substantial dimensional reduction and admitting explicit interpretations, comparing with the vector autoregressive model on the vectorized data. However, the MAR model still encounters difficulties in dealing with large dimensional matrix time series as the coefficient matrices in MAR models are also large. In this paper we propose to achieve further dimension reduction through reduced-rank constraints of the coefficient matrices in the MAR model. Estimation and rank determination procedures are studied. Theoretical investigation and empirical examples show that the reduced-rank constraint can achieve higher statistical efficiency than the MAR model.

We introduce GRACE (the General Regime-Aware Changepoint Estimator), a general, globally exact multiple-changepoint detection and estimation framework in which arbitrary numbers of model parameters may change at or persist across estimated changepoint locations, and all permissible changepoint types and patterns of parameter sharing compete within a single $\ell_0$-penalized optimization. The analyst specifies which types of changepoints are permitted and which parameters each type must preserve, without specifying which changes actually occur, where they occur, or in what order. GRACE jointly estimates the number and locations of changepoints, the type of change at each location, the model fitted between changepoints, and all continuous parameters. As a direct consequence, GRACE can estimate models in which the slope persists across a mean shift. The generality of the framework is achieved through an exact dynamic-programming recursion that retains the accumulated fitting cost conditional on whichever parameters a subsequent change may preserve, tracking multiple parameters jointly when necessary. We establish the global exactness of the recursion and develop functional, penalty-based, and objective-bound pruning rules that eliminate candidates without sacrificing optimality. Ordinary optimal partitioning, FPOP, and CPOP are recovered as special cases, while piecewise-polynomial and seasonal models illustrate the broader range of permissible segment structures and transitions. The resulting framework supports heterogeneous changepoint types, parameter sharing across segments, and substantial parallel computation within a unified approach to exact changepoint estimation.

Estimating causal effects is challenging with observational data due to the lack of exchangeability, and is further complicated with spatial data. In real-life applications such as agricultural and environmental studies, unobserved spatial factors (spatial confounding, SC) and interactions of units in nearby locations (spatial interference, SI) commonly occur jointly, yet existing parametric methods address them separately. We develop a unified framework that treats both simultaneously. We first define the estimand precisely and give an identification result. We then study two estimators. The matching estimator iDAPS integrates neighbourhood exposure and spatial proximity into propensity score matching with balance-optimised weights. We prove a variogram bias bound showing its confounding bias is controlled by the spatial variability of the confounder at the matched distance; this justifies the composite metric, yields a consistency result, and provides a computable diagnostic. The doubly robust estimator recoverU+ augments the propensity and outcome models with the recovered confounder and the exposure; we prove it is doubly robust up to an explicit residual bias from the unrecoverable confounder component. We show that independence-based standard errors are anticonservative under spatial dependence; we provide spatial heteroskedasticity and autocorrelation consistent (HAC), block-bootstrap, and randomisation-based alternatives whose calibration we verify. Every theoretical result is validated numerically. Estimating the effect of selective catalytic and non-catalytic reduction (SCR/SNCR) technologies on ambient ozone reveals no evidence of ozone reduction, while a naive analysis would have delivered a confidently wrong sign. All methods are implemented in the developed open-source R package spaci.

In this paper, one provides a comprehensive mathematical and practical overview of Functional Data Analysis (FDA) specifically applied to parametrized curves in Rp. One observes that curves depending on continuously parameter are naturally present across many fields, such as, for example, monitoring child development in pediatrics, assessing meteorological phenomena, analyzing financial portfolios, tracking neurological functions, and mapping geographic pollution levels. One considers a formal theoretical framework given by a Cartesian product of real separable Hilbert spaces, to model these curves mathematically. To bridge the gap between discrete experimental measurements subject to errors, and smooth continuous functions, the paper details the essential phase of data smoothing and fitting and sets its mathematical formulation via of the Ordinary or Penalized Least Squares criteria which, for the later, using the Sobolev spaces framework, incorporates a smoothing parameter ${\lambda}$ and differential operators to prevent erratic geometric behaviors by penalizing excessive curve roughness. Furthermore, one extends the usual Principal Component Analysis to its functional counterpart in $\mathbb{R}^3$, using the calculus of variations and the Euler-Lagrange multiplier theorem in order to find eigenfunctions and eigenvalues of the covariance operator to exhibit the optimal decomposition of the spatial variance and finally, one highlights the geometric advantages of FDA over traditional multivariate data analysis, emphasizing its unique capacity to capture critical differential features as velocity, acceleration, curvature, and torsion.

We study structural-change testing in multivariate linear regression when the response dimension is proportional to the sample size and the number of predictors is fixed. Despite its relevance to applications across a broad range of fields, this problem remains underexplored. The alternatives of interest allow multiple unknown changes in a prescribed linear contrast of the predictor effects. We construct a least-squares-based Wald statistic standardized by the residual covariance estimator and scan it over candidate change-point segmentations. We propose flexible segment scans for both single and multiple change points, together with a discretized multiscale scan that reduces the computational cost. When the response dimension and sample size diverge proportionally, we establish weak convergence of the normalized statistic process to a centered Gaussian process, yielding implementable critical values for all three scans. We further characterize their asymptotic power under local alternatives, explicitly describing how the signal, design, and high-dimensional aspect ratio determine the limiting power. The finite-sample performance is examined through simulation studies. We apply the proposed methods to filtered and standardized returns from U.S. equity portfolios to investigate structural changes in their exposures to the Fama–French factors.

Hierarchical composite endpoints combining survival and longitudinal functional outcomes are increasingly used in clinical trials, especially when death precludes subsequent functional assessment. The Finkelstein–Schoenfeld strategy analyzes such endpoints through prioritized pairwise comparisons, with survival compared before function. In amyotrophic lateral sclerosis (ALS), this strategy is implemented in the Combined Assessment of Function and Survival (CAFS), which combines survival with the ALS Functional Rating Scale Revised. Although such endpoints provide a clinically meaningful summary of overall treatment benefit, investigators may also want to understand whether the treatment effect is driven by survival, functional outcome, or both. Motivated by the estimand framework, we use ALS-informed simulations from a joint longitudinal–survival model to study settings in which treatment effects on survival and function align or conflict. The simulations show that decomposing the composite win probability into survival and survivor-based functional contributions clarifies their relative roles and separates the composite treatment-benefit question from function-focused questions, including the while-alive comparison and conceptual alternatives based on hypothetical and always-survivor estimands. The functional win probability underlying the while-alive comparison can be subject to survivor-selection bias when treatment affects survival, and inverse-probability weighting can attenuate selection induced by measured predictors under appropriate assumptions. Brief supporting analyses based on principal stratification and multiply robust estimation illustrate the always-survivor estimand. This framework provides practical guidance for reporting and interpreting hierarchical composite endpoints, with CAFS in ALS serving as a concrete motivating example.

We consider the construction of confidence intervals for population means when observations are subject to missingness. To accommodate more general missingness mechanisms than missing completely at random (MCAR), we adopt a reparametrised version of the realisable contamination model of Ma et al. (2026), which is a mixture of an MCAR version and a missing not at random version of the same base distribution $P$. We characterise the minimax length of confidence intervals that can adapt to potentially unknown parameters of the model, including the contamination fraction, for Gaussian base distributions and for nonparametric classes satisfying certain tail or symmetry assumptions. In all of these settings, we provide explicit constructions of simple, practical and finite-sample valid adaptive confidence intervals that attain the corresponding minimax rates. Finally, we provide implications of our results for causal inference.

Comparison of predictive values of diagnostic tests is a topic of interest in Medical Statistics, and has been the subject of different studies. In clinical practice, it is frequent to observe categorical covariates when comparing diagnostic tests. In this framework, a global hypothesis test is proposed to simultaneously compare the predictive values of two diagnostic tests when in all of the individuals categorical covariates are observed. This hypothesis test is solved through regression models and also by weighted least squares method for the analysis of categorical data. Simulation experiments were carried out to study the asymptotic behavior of these methods when a binary covariate is observed and when a covariate with three categories is observed, and these were compared to the behavior of the global test when the covariate is ignored. In general, the method based on regression models has shown to have better asymptotic behavior than the other methods. Furthermore, we studied the application of the method based on the regression models when no covariate is observed, for which the individuals in the sample are randomly assigned to a binary dummy random variable. Simulation experiments carried out showed that this method has greater power than the method without the covariate. The results were applied to two examples.

We propose a class of extended generalized Pareto models for right-censored survival data, with particular emphasis on tail inference and long-term extrapolation. Our framework integrates extreme value theory and survival analysis, combining a generalized Pareto distribution with a flexible perturbation distribution on the unit interval. We consider three perturbation specifications: a parametric Beta model, a Bernstein polynomial estimator, and a histogram-based estimator. To facilitate direct comparison, all three models are fitted using a unified iterative procedure adapted to right censoring through Kaplan-Meier-based pseudo-observations. A Monte Carlo study evaluates finite-sample performance across different tail indices, censoring levels, sample sizes, and model complexities. The results reveal a trade-off between flexibility and stability: the Beta specification generally performs best for tail-index estimation, whereas the histogram estimator performs particularly well for scale estimation under low censoring. The Bernstein estimator shows intermediate performance and greater sensitivity to sample size and censoring. Applications to bladder cancer recurrence and heart-failure survival data show that models with very similar in-sample fits can nevertheless produce markedly different tail-index estimates and long-term extrapolations. These findings emphasize the importance of perturbation specification when extended generalized Pareto models are used for survival extrapolation under censoring.

Chatterjee's estimator uses only two local comparisons per interior observation, leaving a finite-replication variance gap under fixed alternatives. We introduce BRACE, short for blockwise rank aggregation for correlation estimation, which replaces adjacent comparisons with local blocks and averages every within-block rank difference. The block size controls the variance cost of finite local replication. An L2 expansion separates the efficient first-order component of the response-rank statistic from an orthogonal finite-replication component. For an admissible diverging block size, the latter vanishes, so the direct rank estimator attains the information bound. The decomposition yields a consistent variance estimator and Wald confidence intervals under fixed alternatives. At independence, the efficient first-order term vanishes, and the proposed estimator enters a second-order regime in which the same factor controls its null variance.

We study the problem of selecting the extreme (best or worst) population from among $K(\geq 2)$ populations, under the assumption that the extreme population is sufficiently separated from the nearest population. The selection is based on an appropriate measure, which may vary across different application domains. Since the actual value of the measure is unknown, we obtain its estimator using the generalized method of moments under a multistage sampling design. Using this estimator, we propose two sequential procedures, namely online algorithm and multi armed bandit based algorithm. Under suitable regularity conditions and without imposing parametric assumptions on the underlying distributions, both algorithms correctly identify the extreme population with a desired level of confidence. We illustrate the proposed algorithms through applications in econometrics and genetics. In the econometric application, the extreme population is selected using the Gini index as a measure of inequality and the performance of the proposed procedures is assessed through extensive Monte Carlo simulation studies conducted under various distributional settings. In the genetics application, the worst population is identified using a measure derived from the tumor mutation burden (TMB) score and the practical applicability of the proposed algorithms is demonstrated using the Memorial Sloan Kettering-IMPACT 50000 clinical sequencing cohort. Further, we use the proposed framework to identify an anomalous population, provided such a population exists.

Classical continuous-time non-linear filtering fails in generic non-linear state spaces due to an infinite Lie algebraic derivative explosion ($\dim(\mathcal{E}) = \infty$), leading to filter divergence. To resolve this four-decade crisis, we introduce the SMG-Yau-Yau filter and lossless data assimilation framework built on Statistical Fiber Theory over an Orlicz manifold $\mathcal{M}$. By equipping $\mathcal{M}$ with a Riemannian submersion and an Ehresmann connection, the unconstrained Duncan-Mortensen-Zakai score velocity field is orthogonally decomposed into Statistically Verifiable Directions ($\text{SVD}\chi_f$) and Structural Internal Directions ($\text{SID}_f$). System non-linearities and unclosed Lie commutators are orthogonally quarantined in $\text{SID}_f$, protecting macroscopic base parameters from spatial derivative pollution while preserving total score variance energy. We unify the asymptotics through a Dual-Axis Collapse Mechanism: proving our model identically recovers classical Yau-Yau dynamics when $\dim(\mathcal{E}) < \infty$, while large-sample limits ($N \to \infty$) induce a thermodynamic quench that flattens infinite-dimensional geometry under $\dim(\mathcal{E}) = \infty$. Finally, we formulate the Active Acausal Tension (AAT) functional to monitor accumulated model misspecification online. Exceeding a topological capacity threshold triggers Gauge Symmetry Breaking (GSB), which dynamically expands base coordinates ($d \to d+1$) to ensure non-asymptotic stability and convergence to the exact state density.