Papers

Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with causal estimator performance may differ across performance measures. We studied this question in a partially linear model using Monte Carlo simulations. We compared ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost), evaluating nuisance-function prediction error, bias, RMSE, and 95% confidence interval coverage. We also examined a simple joint-error measure based on the absolute cross-product of estimation errors from the exposure and outcome nuisance functions. Across the simulated settings, XGBoost had the lowest RMSE among the non-oracle methods, while DML-XGBoost generally provided better confidence interval coverage. Prediction error did not consistently track causal bias across methods and settings, and the method with the best point-estimation performance did not necessarily have the best confidence interval coverage. The joint-error measure was only weakly associated with causal bias and did not provide a useful standalone measure of causal performance. These results suggest that prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.

We introduce a robust clustering method, MK-means DPD, that estimates cluster centers and covariance matrices using density power divergence (DPD) measures combined with Mahalanobis distance, making it resistant to outliers and adaptable to heterogeneous, elliptical clusters, unlike the classical K-means algorithm. Since Mahalanobis distance-based K-means lacks a general convergence guarantee, we further introduce a convergent variant, Density-Consistent MK-means DPD (DC-MK-means DPD), which redefines the cluster assignment step in terms of a pointwise DPD loss. We prove a formal theorem establishing that the resulting algorithm converges in a finite number of steps. We also propose two new robust internal evaluation indices, a Median Davies-Bouldin Index and a Trimmed Calinski-Harabasz Index, to ensure that performance comparisons are not themselves distorted by outliers. The efficacy of the proposed methods is demonstrated on simulated data, showing superiority over existing methods, and on two real datasets: Iris data, to identify similar species, and COVID-19 case fatality rate and infection rate data for countries worldwide, examining the resulting clusters' geographic and socio-economic patterns.

Integrals of spectral densities are frequently used to summarize spectral characteristics of linear processes. This work studies self-normalization for estimators of such integrals based on sequential periodograms and establishes weak convergence of the corresponding processes. For linear functionals of the spectral density, self-normalization yields pivotal limiting distributions that are free of unknown spectral quantities. For non-linear functionals, however, additional components with distinct covariance structures may arise in the limiting process. We demonstrate this phenomenon for the integrated squared spectral density.

Compositional data are positive multivariate data whose sum equals 1. A popular method to analyze such data is via log–ratio transformations, which are however not applicable when zero values are present. In this paper we present a conditional logistic normal distribution suitable for compositional data with structural zero values. The model is applicable to arbitrary dimensions and the EM algorithm guarantees a fast implementation. The model accepts predictors and we provide a residual analysis. We further provide principal component analysis and biplots for visualization of compositional data with zero values present. Simulation studies and real data examples illustrate the performance of the model, with and without covariates, and compare it to the Dirichlet analogue.

Via Computational Taxonomy (CT), we develop Design of Experiment(DoE) based on rigorously redefined constituting ingredients of complex system dynamics: randomness, nonlinearity and even class, through a data-driven constructed Taxonomic Hierarchy. As an opposite quest of Classification without man-made assumptions and structures, we illustrate this new perspective of DoE through a civil engineering complex system: Concrete Compressive Strength (CCS). CT begins by building a Taxonomic Hierarchy as a heterogeneity-vs-homogeneity map framed with a tree geometry to represent CCS-system dynamics. At each internal node of this hierarchy, a heatmap is computed via Scientific Data Analysis (SDA) to reveal locality-embraced heterogeneity through block structured covariate homogeneity annotated with response's locality-split. Only arriving at each ending-node of this hierarchy, coherence of homogeneity is achieved on both response and covariate sides. As such a class of finite sample nature is computationally recognized and confirmed. In contrast, nonlinearity is evidently observed as incoherence of response-vs-covariate homogeneity when comparing two classes located on two distinct branches. This hierarchy explicitly maps out system's randomness and nonlinearity to serve as a scientific basis for any DoE quest. Design of Experiment (DoE) for any designated class is redefined as a search for a covariate subspace that embraces the class-representative randomness and at the same time avoids potential nonlinearities with respect to the rest of classes. This is a brand-new theme of DoE.

Multilinear principal component analysis (MPCA) reduces the dimension of tensor-valued data while preserving their mode-specific structure, but its quadratic scatter criterion can be unstable under heavy-tailed distributions and contamination. We propose spatial-sign-based multilinear principal component analysis (SMPCA), a robust dimension-reduction method that centers the observations by their spatial median, removes radial magnitude through spatial-sign normalization, and estimates the mode-wise loading spaces by alternating eigendecompositions. Under a separable tensor elliptical model, we show that the target mode-wise loading spaces uniquely maximize the population criterion and that one complete sweep of exact population block updates recovers them from any initialization. We also characterize exactly when their tensor-product subspace coincides with a leading unrestricted subspace of vectorized spatial-sign PCA and, when finite second moments exist, ordinary vectorized PCA. At the sample level, we derive explicit statistical rates for the mode-wise subspaces and the joint multilinear projector, obtain corresponding reconstruction guarantees, establish consistency of the cumulative-contribution dimension selector, and prove that the objective values generated by exact cyclic updates are nondecreasing and convergent. Simulations and an empirical application show that SMPCA is more accurate and stable than competitors under heavy-tailed distributions and outlier contamination, while retaining competitive performance under light-tailed settings.

Win statistics require a prespecified outcome hierarchy. Clinical teams sometimes agree only on the highest priority outcome, leaving the order of lower priority outcomes unresolved, and clinically meaningful thresholds may be specified as ranges. Separate sensitivity analyses describe how the results change. A single inference for the full set of planned analyses is generally absent. We define the estimand as the smallest net benefit among the comparison rules allowed by the protocol or statistical analysis plan. Each rule uses the usual two-sample U-statistic. Large-sample results are developed for a finite list of rules and for a continuous threshold range. Inversion of an intersection-union test gives a one-sided lower confidence bound, with no multiplicity adjustment for the single claim that every individual net benefit is positive. Simulations show valid one-sided coverage and illustrate the gap between a favorable result for one selected hierarchy and a favorable result across all prespecified hierarchies. An application to ACTG 175 shows how the ordering of laboratory outcomes can affect the strength of the conclusion. A further example identifies an unfavorable threshold that is missed by a sparse grid.

We derive the complete duality theory underlying the Hodrick–Prescott filter, whose rank-deficient second-difference penalty admits infinitely many equivalent trend representations via generalized inverses. Constructing two canonical choices—the Moore–Penrose-based B-representation and an alternative A-representation—we prove that the extracted trend is invariant across representations, obtain a closed-form Bregman-type divergence quantifying their disagreement under a shared coefficient vector, and show this divergence vanishes as $\lambda\to\infty$. We further mollify the non-smooth $\ell_1$ trend filter with a compactly supported biweight kernel to obtain a closed-form $C^3$ Convolutional LASSO that restores Newton-type quadratic convergence without sacrificing the kink- setecting character of $\ell_1$ regularization. Theoretical results are verified numerically and benchmarked against ADMM/IRLS on NVIDIA's 2013–2018 daily closing prices, where the sparse filter isolates genuine growth-regime breaks—chiefly the November 2016 post-earnings acceleration—cleanly separated from the smooth $L_2$ trend.

Understanding why a target metric changes is a fundamental problem in data-driven decision making, beyond anomaly detection alone. We study root cause attribution for metric changes in complex e-commerce systems, focusing on trade-offs between interpretability, efficiency, and causal validity. As a starting point, we extend a metric-decomposition method into a recursive metric-tree framework for multi-level root cause analysis, but this relies on independence and decomposability assumptions that miss complex causal dependencies. In contrast, graphical causal models (GCMs) relax these assumptions and improve causal validity, at the cost of interpretability, higher computational and data demands, and potential attribution target misalignment. Through real-world applications, mathematical proofs, and simulations, we characterize the fundamental sources of these trade-offs. Guided by these insights, we propose a unified, causally informed attribution approach that integrates structural causal information into the metric-tree decomposition framework and corrects key sources of misalignment in GCM-based causal attributions, substantially improving causal validity while preserving interpretability and fast computation. Analytical proofs and simulations demonstrate that the proposed approach produces more accurate root cause attributions, and we also present a real-world application.

In this article, we revisit the problem of group factor analysis and propose a one-step penalized least squares method to estimate the factor loadings and factors in large-dimensional group factor models, offering a distinct alternative to the conventional two-step principal component approach. Our procedure originates from the equivalence between the group factor structure and the carefully tailored identification conditions. Leveraging this insight, we develop a tricky Lagrange multiplier formulation for a penalized least square loss function. This one-step optimization framework, combined with the fine-tuned penalty parameters, facilitates the direct derivation of central limit theorems for factor loadings, factor scores, common and local components, as well as the convergence rates for them. Our theory demonstrates that our one-step approach achieves the same rate as the two-step aggregated principal-component method and even the same limiting standard error in the balanced group panel case, but smaller limiting standard error than the two-step canonical correlation procedure. Extensive simulation studies justify the theory. Applications to U.S. house prices and CSI300 weekly returns confirm that our method identifies global factors and heterogeneous local patterns.

Functional clustering is an important tool for identifying latent heterogeneity in functional data and has been widely applied across various scientific fields. However, many existing methods are not fully adaptive, as they may require the number of clusters to be prespecified and may lack automatic control over the smoothness of the underlying functions. They also commonly assume independent and identically distributed errors, thereby overlooking additional within-curve dependence. We propose a fully adaptive Bayesian procedure for functional clustering that addresses these limitations through Dirichlet process priors, adaptive smoothness control, and flexible covariance modeling. For computational scalability, the proposed method employs variational inference as an efficient alternative to Markov chain Monte Carlo. Together, these features provide a unified Bayesian framework for functional clustering and cluster-specific mean function estimation in the presence of structured within-curve dependence.

A continuous clinical measurement recorded in fixed physical units may have different prognostic meaning across patients when its effect depends on a patient-level modifier. For example, the same tumor diameter may imply markedly different prognosis in an infant and an adult, because patient size can modify its prognostic effect. We formalize this problem through prognosis-equivalent mapping for time-to-event outcomes. The resulting estimand maps a measurement value observed at one modifier level to the value under a reference modifier level that yields the same conditional prognostic quantity. The basic operation is to equate a monotone conditional prognostic score and invert the reference-side curve. In observational data, however, treatment may be selected according to the modifier and the measurement, so a direct equate-and-invert procedure may reflect differences in treatment assignment as well as the prognostic meaning of the measurement itself. We therefore define, in addition to a direct approach, a policy-standardized mapping that standardizes treatment under a common policy using the g-formula. We also introduce an origin-referenced mapping that compares changes in prognostic score from a common anchor, thereby separating modifier-specific prognostic levels from modifier dependence in the measurement–prognosis relationship. Using Cox models, we develop linear and flexible inversion estimators with analytic and bootstrap confidence bands. Simulations evaluate finite-sample performance and illustrate how treatment standardization and origin referencing clarify what is being mapped.

Deployed decisions are often optimized once and retained because updates impose operational, regulatory, or switching costs. As operating conditions change, when should such decisions be re-optimized? We study this question for stochastic optimization when the objective's functional form is known but the decision maker's trade-offs are encoded by an unknown preference parameter. Standard distribution-shift tests are poorly aligned with this goal: they can flag detectable yet decision-irrelevant changes without determining whether the incumbent decision has become materially suboptimal. We propose RADAR (Regret-based Assessment of Decision Adequacy and Risk), a decision-focused framework that uses inverse optimization to infer latent preferences and tests the deployed decision's optimality gap under the current distribution. By targeting regret, RADAR ignores decision-irrelevant shifts while detecting changes that warrant re-optimization. We develop two-sample and sequential changepoint procedures and establish asymptotic guarantees for Type-I error and power. Across synthetic optimization problems, a semi-synthetic capacity allocation task, and police-zone planning, RADAR more reliably distinguishes harmful from harmless shifts than decision-agnostic alternatives.

A new approach to robust estimation in generalized linear models is introduced. The idea of the method is to first transform the responses applying the composition of the normal quantile function and the probability integral transformation. Then, using that the transformed responses should follow a standard normal distribution, find the values of the parameters that minimize a robust measure of their size. In practice an approximation of this transformation is used. The proposed estimators are studied theoretically for distributions that depend on a single parameter and through simulations and examples for the particular cases of Poisson and logistic regression.

Varmapack is a software package for efficient, exact simulation of VARMA time series without a burn-in period. For stationary models, Varmapack can generate initial states and innovations from their joint stationary distribution. Alternatively, the user can supply initial states, in which case innovations are generated from their conditional distribution. The core C library has interfaces to R, Python, and Matlab. It also offers VARMAX simulation and computation of autocovariances and correlations, spectral radii, and impulse responses. Varmapack automatically selects between vector-Yule-Walker and state-space methods for covariance computation and uses level-3 BLAS operations for efficient generation of multiple replicates. Benchmarks on several platforms show substantial performance gains over existing simulation software, ranging from several-fold to more than three orders of magnitude for the packages and models considered. Varmapack is open source and publicly available through GitHub.

The Bayes factor (BF) is a central tool in Bayesian hypothesis testing and model selection, yet its practical use is often challenged. Classical BFs depend heavily on prior specification, cannot be applied with improper priors, and are typically interpreted through arbitrary evidence scales. Moreover, they fail to capture uncertainty inherent in the data, leading to an analogy with frequentist p-values, and primarily reflect prior-predictive rather than posterior-predictive performance. We introduce the stochastic Bayes factor (SBF), a new framework that extends the BF by explicitly incorporating uncertainty via replicated data. Formally, the SBF is defined as a push-forward measure transferring the BF from the observed data space to that of replications. This approach generalizes previous calibration proposals, while emphasizing posterior-predictive replication as a robust alternative. We establish key theoretical properties, including model consistency, compatibility and dominance, ensuring that SBFs preserve desirable Bayesian guarantees. An algorithmic routine is then proposed to operationalize the SBF, guiding model discrimination in a principled way while naturally providing model calibration. Simulation studies and real applications confirm that the SBF offers improved robustness and predictive reliability compared to the classical BF, by providing a valuable tool for model comparison.

We consider the problem of feature selection in linear models with finite-sample control of the false discovery rate (FDR). While existing knockoff-based methods control the directional FDR, which penalises incorrect sign estimates, they do not target discoveries in a pre-specified direction, and their knockoff constructions are entirely response-agnostic. We introduce the response-guided knockoff filter, which leverages a noise-perturbed version of the response to guide knockoff construction toward features likely to have the target sign, while provably controlling the directional FDR. The method operates under a weaker sample-size requirement $n > p + 2$, compared to $n \geq 2p$ required by existing fixed-X generators. Simulations and HIV drug resistance experiments demonstrate power gains over existing methods.

Mean-tilted intervals (MTIs) provide a fixed-content family of interval targets indexed by retained-mean balance. This paper develops generalized-Bayes computation for using those targets in regression and time-varying endpoint models after content and tilt have been specified. The update combines a prior with an exponentiated residual-product check loss, yielding uncertainty summaries for endpoint functions rather than a response-distribution model. A pseudo-asymmetric-Laplace normal-exponential representation gives generalized-inverse-Gaussian latent-scale updates and Gaussian conditional updates for one root when the other is fixed. The same representation gives deterministic ECM equations for generalized-posterior modes. We present ridge endpoint regression, a conditionally Gaussian shrinkage construction for the zero-tilt case, deterministic fixed-feature readouts, and dynamic linear endpoint states updated by alternating forward-filtering backward-sampling steps. These methods extend the MTI target from iid intervals to regression and dynamic settings; tolerance certification and response prediction require separate calibration or response models.

An analyst should not assume that a design score improves a meta-analysis simply because it is labeled as robustness. This paper treats declining heterogeneity along a prespecified, outcome-separated design score as a falsifiable directional hypothesis. In an 18-study illustration, the constrained model lands at $\gamma = 0$ and becomes numerically identical to conventional random effects, while the unrestricted scale fit points in the opposite direction. Simulations that deliberately violate the restriction show the same graceful fallback under wrong-direction and U-shaped heterogeneity; a stepwise decreasing variance function retains an efficiency gain despite functional-form misspecification. DR-Meta formalizes the hypothesis as $\tau^2(\mathrm{DR}) = \tau_0^2 \exp(-\gamma \mathrm{DR})$, $\gamma \geq 0$, within an established location-scale framework. Exact nesting, conditional weight monotonicity, a fixed-effect upper bound, pseudo-true targets under mean misspecification, and score-rescaling behavior are derived with full proofs. Efficiency gains are negligible around an empirically anchored $\gamma$ near 1 and become material only under stronger gradients; the largest RMSE reduction, about 9.6 percent, occurs in a deliberately extreme condition. Plug-in intervals under-cover relative to random effects, and modified Knapp-Hartung adjustment improves coverage only modestly. Widening the $\gamma$ optimization bound changes $\gamma$ estimates much more than pooled-estimate RMSE. The practical contribution is therefore diagnostic rather than automatic efficiency: a nested directional restriction can be supported, contradicted, or collapse transparently to random effects, provided constrained, unrestricted, location, and sensitivity analyses are reported together.

Cluster randomized trials (CRTs) can exhibit informative cluster sizes (ICS) where cluster size is associated with outcomes and/or treatment effects. Under ICS, the individual and cluster-average treatment effects (iATE, cATE) can diverge, and the conventional linear mixed-effects model (LMM) and generalized estimating equation (GEE) with an exchangeable working correlation can produce data-dependent weighted contrasts that are not consistent for either estimand. In these settings with ICS, we propose easy to implement "cluster-size saturated models with g-computation" (CS-g), which employ a simple two-step adjustment to standard practice: (1.) augment the appropriately weighted working LMM or GEE with a saturated continuous cluster-size main effect and treatment x cluster-size interaction, and (2.) apply g-computation to target an interpretable marginal estimand. We prove that the appropriately weighted cluster-size saturated LMM with g-computation and more general cluster-size saturated GEE with g-computation can consistently target the iATE and cATE, among a broad class of interpretable estimands, while allowing for ICS. Crucially, this consistency holds under arbitrary misspecification of other model components, including the functional form of the saturated cluster-size terms. Furthermore, we demonstrate exact finite-sample equivalence between these consistent CS-g estimators and their model-robust standardization counterparts. Across simulations with continuous and binary outcomes, the proposed CS-g estimators were unbiased, more efficient than other consistent estimators, and returned greater power to detect ICS. A re-analysis of the PPACT P-CRT further illustrates the approach. Altogether, CS-g offers a simple, robust, and efficient route to target interpretable marginal effects in P-CRTs with ICS.

Modeling multivariate extremes using a geometric perspective leverages the shape of the multivariate point cloud to make inference on joint tail probabilities. While the original statistical framework for geometric extremes was fully parametric, relying on a gauge function that uniquely defines the shape for a given density, newer methods have introduced semi- and non-parametric alternatives to increase flexibility. We propose a modeling approach that retains the simplicity of the parametric framework but adds flexibility by using Bayesian model averaging (BMA) to improve prediction of tail risk probabilities. In contrast to previous works that use a truncated radial likelihood, we propose using a censored likelihood, which we find has consistently better performance in terms of predictive mean squared error, particularly in small-sample settings, although at the expense of increased bias. To generate predictions, we use a simple importance sampling scheme that seems to match the accuracy of more bespoke methods. Finally, we apply our approach to two fire weather indices, which are designed to capture somewhat orthogonal aspects of fire risk, to illustrate our method's practical utility in environmental applications.

Prognostic factor evaluation and prediction model development are central to precision oncology, enabling patient risk stratification and individualized treatment selection. Unified predictions that synthesize information from existing models are valuable for comprehensive and consistent risk assessment. Many studies also seek to evaluate the incremental value of new biomarkers beyond established prognostic factors. However, such efforts are often constrained by small-to-moderate sample sizes. Motivated by these challenges, we consider Cox regression analysis in settings where individualized risk predictions from existing models are externally available without a transparent or interpretable structure, for example, through online calculators. We develop a Bayesian discretized survival time inference framework in which individualized predictions from potentially multiple external sources are integrated through a formulation based on Kullback-Leibler divergence, yielding informative priors. The divergence-based formulation serves as a surrogate for the external information likelihood, enabling principled incorporation of individualized predictions without requiring knowledge of the underlying external prediction models. Theoretical results show that the resulting posterior mean estimators are asymptotically more efficient than their internal-only maximum likelihood counterparts. However, using the divergence-based surrogate in place of the unavailable external likelihood renders posterior variance-based inference conservative. We propose a correction to address this overcoverage. We demonstrate the performance of the proposed approach through simulations and an application to prostate cancer trial data.

Under a model-assisted framework, a penalized logistic generalized regression estimator is developed to estimate a finite population proportion from complex survey data and auxiliary data. The proposed estimator controls the impact of unnecessary auxiliary variables through a lasso or ridge penalty. A central limit theorem is derived for the penalized regression coefficients and for the penalized logistic generalized regression estimator. Through simulations, it is shown that including the penalty increases the efficiency of the estimator when the true model is sparse. An example using United States Forest Service data demonstrates the applicability of the estimator for surveys with many available auxiliary variables.

Incomplete adjudication and endpoint misclassification arise when gold-standard event classification is available only for an internal validation sample. With accurate follow-up times and covariates but error-prone event indicators, naive Cox regression can be biased and inverseprobability weighting inefficient. We develop orthogonal validation-augmented Cox (OVAC) regression, a cross-fitted augmented Cox estimator for incomplete failure indicators. OVAC replaces the missing event indicator with a cross-fitted augmented pseudo-event and explicitly retains the first-order contribution from estimating the Cox risk-set mean. The same term emerges from projection of the full-data influence function through the validation mechanism, linking the score expansion to the observed-data efficient influence function. The score exhibits exact product-form nuisance drift, yielding double-robust identification, Neyman orthogonality, and root-n inference under product-rate conditions. In 1,000 R replications, full-variance SE/SD ratios were 0.997 and 0.992, with 95% coverage of 0.955 and 0.948. A 200-replication diagnostic showed that the risk-set term alone was 77.8% and 81.1% of the full-SE magnitude, although covariance cancellation made its net SE effect smaller than 0.3%. In a 250-replication method comparison, OVAC reduced empirical variance by 38.8% and 37.7% relative to IPW. OVAC provides machine-learning-compatible Cox estimation with explicit risk-set linearization, calibrated inference, and validation-design guidance.

Borrowing external control data can improve the efficiency of clinical trials, particularly when patient accrual is difficult. A persistent challenge is how to prespecify the degree of borrowing systematically and transparently. In practice, prior weights are often selected heuristically or calibrated through simulation to achieve desired operating characteristics, making them difficult to justify scientifically. Moreover, patient-level covariate data from external sources are rarely available when the new trial is designed, precluding patient-level adjustment methods. We propose CARB (Covariate-Assessed Robust Borrowing), a framework that formalizes prior-weight specification as a design-stage assessment of baseline compatibility. Using only aggregate information, CARB quantifies discrepancies in prespecified baseline covariates between the new trial and each external source, without using outcome data from the new trial. A prespecified mapping translates the resulting dissimilarity measure into a source-specific prior weight on the exchangeable component of a robust borrowing model. Simulation studies show that CARB reduces bias and type I error inflation relative to fixed borrowing under observed and unobserved incompatibility, while improving efficiency when external controls are compatible. An application to advanced melanoma trials illustrates covariate-informed borrowing from multiple historical sources. An apparent discrepancy in reported baseline characteristics serves as a warning signal that reduces borrowing. CARB provides a transparent and reproducible way to borrow cautiously when patient-level covariate data from external sources are unavailable.

Many observational studies evaluate the risks and benefits of time-varying interventions. In these longitudinal settings, the primary outcome of interest is often a clinical event that is precluded by mortality, which acts as a competing risk. Evaluating dynamic treatment regimes (DTRs) is complicated by time-varying confounding, right-censoring, and progressive sample size reduction over time, for which traditional methods such as the g-formula or inverse probability weighting may be misspecified or highly unstable. In this work, we develop the nonparametric efficiency theory and derive the efficient influence function for the cumulative incidence of an event under a DTR in the presence of a competing risk and right-censoring. Building on this result, we propose a sequentially doubly robust estimator that accommodates flexible machine learning for nuisance estimation while retaining root-n consistency and asymptotic normality. We illustrate the utility of our framework by estimating long-term cumulative incidence of clinical fractures under different bisphosphonate "drug holiday" regimes for osteoporosis.

Synthetic data can improve statistical inference when real data are scarce, but naively treating synthetic samples as real data can introduce bias and lead to unreliable inference. We develop a general framework for synthetic-augmented inference across a population of related tasks. It characterizes synthetic augmentation by the number of synthetic observations and their weight. Central to our framework is a size-weight frontier that specifies, for each weight, the largest synthetic sample size for which all smaller sizes attain the target task-marginal coverage. We estimate this frontier from historical tasks, and establish a finite-sample coverage guarantee simultaneously for all size-weight configurations on or below the estimated frontier. In experiments using large language model responses to augment opinion survey data, our procedure achieves target coverage and substantially narrows confidence intervals.

Relational Event Models (REMs) provide valuable insights into the dynamics of longitudinal social networks. Yet, the vast availability of potential predictors for a dyad's event rate poses the risk of selecting irrelevant variables and specifying an overfitted model that does not generalize to new data. Despite the recent popularity of Bayesian regularization methods to address this, there has not been a systematic evaluation of the performance of Exact Bayesian Regularization (EBR) and Approximate Bayesian Regularization (ABR) against standard Maximum Likelihood (ML) procedures commonly used for REMs. To address this, we conduct a simulation study in which directed Relational Event History (REH) data is generated with endogenous and exogenous effects of varying strength and compare the performance of (a) unregularized ML estimation, (b) ABR through normal approximations of the likelihood with Ridge and Horseshoe priors, and (c) EBR with Horseshoe priors. We find that threshold-based criteria applied to ABR and EBR with Horseshoe priors outperform univariate selection using p-values from ML estimation in variable selection accuracy. Regarding predictive performance, ABR with Ridge priors and EBR with Horseshoe priors outperform ML REMs, particularly for small sample sizes. Given only small gains with large computational burdens when using EBR, we therefore advise researchers to use ABR with a suitable prior.

In applications, it is often required to test objects or people to determine their qualities in terms of certain metrics. However, besides being naturally noisy, the test results can be corrupted by adversarial behaviors of objects or people being tested (test takers). For example, dishonest test takers can cheat in the exams to distort the test results. With the development of AI technologies, such distortions driven by cheating using AI technologies are becoming more commonplace and severe. In this paper, we propose optimal testing strategies which can still recover needed test results even if there are cheaters polluting the results. The proposed testing strategies will optimally re-test selected group of test takers using different testing security measures. We determine the optimal testing strategies using a dynamic programming method.

This paper investigates whether five fold cross fitting improves nonresponse adjustment in survey estimation when flexible machine learning methods are used to estimate response propensities. We conduct a finite population Monte Carlo simulation with 90 experimental configurations and 2,000 replications per configuration, varying sample size, response rate, and the structure of the response mechanism. Logistic regression is used as a conventional parametric benchmark, while Random Forest and Gradient Boosting Machine are considered as flexible nonparametric models.