Papers

Clustered data arise naturally in many scientific and applied research settings where units are grouped within clusters. Such data are commonly analyzed using linear mixed models to account for within-cluster correlations. This article proposes a proportional random effect block bootstrap applicable to general linear mixed model settings with imbalanced cluster sizes, both random intercepts and random slopes, and autocorrelation within clusters, while allowing for non-normal random effect and error distributions. It generalizes the original random effect block bootstrap, which was developed for more restrictive settings with balanced cluster sizes, random intercepts only, and constant within-cluster correlation. The proposed bootstrap is shown to be Fisher consistent under these more general settings. Simulations demonstrate strong finite sample inferential performance relative to the original random effect block bootstrap and several existing bootstrap methods for clustered data across a variety of scenarios. Application to the Mayo Clinic primary biliary cirrhosis dataset, which contains cluster sizes ranging from 1 to 16 and exhibits evidence of within-cluster autocorrelation and non-normality, further illustrates improved bootstrap confidence intervals using the proposed method.

We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$ is an inhomogeneous Markov chain satisfying some mixing assumptions and $f_j$ is a sequence of sufficiently regular functions. Even though the case of non-stationary chains and time dependent functions $f_j$ is more challenging, our results seem to be new already for stationary Markov chains. They also seem to be new for non-stationary Bernoulli shifts (that is when $(X_j)$ are independent but not identically distributed). This paper is the first one in a series of two papers. In \cite{Work} we will prove local limit theorems including developing the related reduction theory in the sense of \cite{DolgHaf LLT, DS}.

Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient protection or overly conservative and costly solutions. Recent approaches using conformal prediction construct data-driven uncertainty sets with finite-sample coverage guarantees, but they still fix coverage targets a priori and offer little guidance for selecting robustness levels. We propose a new framework that provides distribution-free, finite-sample guarantees on both miscoverage and regret for any family of robust predict-then-optimize policies. Our method constructs valid estimators that trace out the miscoverage–regret Pareto frontier, enabling decision-makers to reliably evaluate and calibrate robustness levels according to their cost–risk preferences. The framework is simple to implement, broadly applicable across classical optimization formulations, and achieves sharper finite-sample performance. This paper offers a principled data-driven methodology for guiding robustness selection and empowers practitioners to balance robustness and conservativeness in high-stakes decision-making.

We propose an iterative Gaussianization method for sampling from unnormalized densities by repeatedly applying mean-field variational inference (MFVI) in rotated coordinate systems. At each iteration, the method selects a rotation, solves an MFVI subproblem in the rotated coordinates, and applies the inverse coordinatewise map to transform the current target closer to the standard Gaussian. The resulting algorithm provides a computationally efficient way to construct flow-like transport maps: it requires only MFVI subproblems, avoids large-scale optimization, and produces transformations that are easy to invert and evaluate. The effectiveness of the procedure depends on selecting informative rotations. We develop an efficient PCA-type method that chooses rotations from the leading eigenvectors of a cross-covariance matrix involving the target's score function. Experiments on Bayesian posterior sampling tasks show that performing MFVI in the proposed PCA-rotated coordinate systems substantially improves over standard MFVI, and that the resulting iterative Gaussianization procedure provides accurate flow-like approximations at lower computational cost than conventional normalizing-flow variational approximations.

Spatial variable genes (SVGs) reveal critical information about tissue architecture, cellular interactions, and disease microenvironments. As spatial transcriptomics (ST) technologies proliferate, accurately identifying SVGs across diverse platforms, tissue types, and disease contexts has become both a major opportunity and a significant computational challenge. Here, we present a comprehensive benchmarking study of 20 state-of-the-art SVG detection methods using human slides from STimage-1K4M, a large-scale resource of ST data comprising 662 slides from more than 18 tissue types. We evaluate each method across a range of biologically and technically meaningful criteria, including recovery of pathologist-annotated domain-specific markers, cross-slide reproducibility, scalability to high-resolution data, and robustness to technical variation. Our results reveal marked differences in performance depending on tissue type, spatial resolution, and study design. Beyond benchmarking, we construct the first cross-tissue atlas of SVGs, enabling comparative analysis of spatial gene programs across cancer and normal tissues. We observe similarities between pairs of tissues that reflect developmental and functional relationships, such as high overlap between thymus and lymph node, and uncover spatial gene programs associated with metastasis, immune infiltration, and tissue-of-origin identity in cancer. Together, our work defines a framework for evaluating and interpreting spatial gene expression and establishes a reference resource for the ST community.

Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model performance on the test set, and averages the model performance across different data splits. A well-known criticism is that such cross-validation procedure does not directly estimate the performance of the particular model recommended for future use. In this paper, we propose a new method to estimate the performance of a model trained on a specific (random) training set. A naive estimator can be obtained by applying the model to a disjoint testing set. Surprisingly, cross-validation estimators computed from other random splits can be used to improve this naive estimator within a random-effects model framework. We develop two estimators – a hierarchical Bayesian estimator and an empirical Bayes estimator – that perform similarly to or better than both the conventional cross-validation estimator and the naive single-split estimator. Simulations and a real-data example demonstrate the superior performance of the proposed method.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.

Chronic diseases frequently co-occur in patterns that are unlikely to arise by chance, a phenomenon known as multimorbidity. This growing challenge for patients and healthcare systems is amplified by demographic aging and the rising burden of chronic conditions. However, our understanding of how individuals transition from a disease-free-state to accumulating diseases as they age is limited. Recently, data-driven methods have been developed to characterize morbidity trajectories using electronic health records; however, their generalizability across healthcare settings remains largely unexplored. In this paper, we conduct a cross-country validation of a data-driven multimorbidity trajectory model using population-wide health data from Denmark and Austria. Despite considerable differences in healthcare organization, we observe a high degree of similarity in disease cluster structures. The Adjusted Rand Index (0.998) and the Normalized Mutual Information (0.88) both indicate strong alignment between the two clusterings. These findings suggest that multimorbidity trajectories are shaped by robust, shared biological and epidemiological mechanisms that transcend national healthcare contexts.

Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as powerful priors for solving such problems. However, existing methods either rely on projection-based techniques that enforce measurement consistency through heuristic updates, or they approximate the likelihood $p(\boldsymbol{y} \mid \boldsymbol{x})$, often resulting in artifacts and instability under complex or high-noise conditions. To address these limitations, we propose a novel framework called coupled data and measurement space diffusion posterior sampling (C-DPS), which eliminates the need for constraint tuning or likelihood approximation. C-DPS introduces a forward stochastic process in the measurement space $\{\boldsymbol{y}_t\}$, evolving in parallel with the data-space diffusion $\{\boldsymbol{x}_t\}$, which enables the derivation of a closed-form posterior $p(\boldsymbol{x}_{t-1} \mid \boldsymbol{x}_t, \boldsymbol{y}_{t-1})$. This coupling allows for accurate and recursive sampling based on a well-defined posterior distribution. Empirical results demonstrate that C-DPS consistently outperforms existing baselines, both qualitatively and quantitatively, across multiple inverse problem benchmarks.

It is increasingly important to generate synthetic populations with explicit coordinates rather than coarse geographic areas, yet no established methods exist to achieve this. One reason is that latitude and longitude differ from other continuous variables, exhibiting large empty spaces and highly uneven densities. To address this, we propose a population synthesis algorithm that first maps spatial coordinates into a more regular latent space using Normalizing Flows (NF), and then combines them with other features in a Variational Autoencoder (VAE) to generate synthetic populations. This approach also learns the joint distribution between spatial and non-spatial features, exploiting spatial autocorrelations. We demonstrate the method by generating synthetic homes with the same statistical properties of real homes in 121 datasets, corresponding to diverse geographies. We further propose an evaluation framework that measures both spatial accuracy and practical utility, while ensuring privacy preservation. Our results show that the NF+VAE architecture outperforms popular benchmarks, including copula-based methods and uniform allocation within geographic areas. The ability to generate geolocated synthetic populations at fine spatial resolution opens the door to applications requiring detailed geography, from household responses to floods, to epidemic spread, evacuation planning, and transport modeling.

In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to the widespread coexistence of diverse interactions in social, industrial, and biological domains. This motivates the development of a rigorous and readily applicable framework for studying properties of large multiplex networks. In this article, we provide a self-contained introduction to the limit theory of dense multiplex networks, analogous to the theory of graphons (limit theory of dense graphs). As applications, we derive limiting analogues of commonly used multiplex features, such as degree distributions and clustering coefficients. We also present a range of illustrative examples, including correlated versions of Erdős-Rényi and inhomogeneous random graph models and dynamic networks. Finally, we discuss how multiplex networks fit within the broader framework of decorated graphs, and how the convergence results can be recovered from the limit theory of decorated graphs. Several future directions are outlined for further developing the multiplex limit theory.

Generative models form the backbone of modern machine learning, underpinning state-of-the-art systems in text, vision, and multimodal applications. While Maximum Likelihood Estimation has traditionally served as the dominant training paradigm, recent work have highlighted its limitations, particularly in generalization and susceptibility to catastrophic forgetting compared to Reinforcement Learning techniques, such as Policy Gradient methods. However, these approaches depend on explicit reward signals, which are often unavailable in practice, leaving open the fundamental problem of how to align generative models when only high-quality datasets are accessible. In this work, we address this challenge via a Bilevel Optimization framework, where the reward function is treated as the optimization variable of an outer-level problem, while a policy gradient objective defines the inner-level. We then conduct a theoretical analysis of this optimization problem in a tractable setting and extract insights that, as we demonstrate, generalize to applications such as tabular classification and model-based reinforcement learning. We release the code at https://github.com/abenechehab/nll_to_po .

Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on transformations, which may induce substantial bias near the simplex boundary. We propose a nonparametric mixture-based framework for density estimation on compositions. Nonparametric Dirichlet mixtures are employed to naturally accommodate boundary values, thereby avoiding the transformation or zero-replacement, while also identifying components supported on the boundary, providing reliable estimates for data with zero or near-zero values. Bandwidth selection and initialization schemes are addressed. For comparison, nonparametric Gaussian mixtures, coupled with log-ratio transformations, are also considered. Extensive simulations show that the proposed estimators outperform existing approaches. Three real data applications, including GDP data analysis, handwritten digit recognition, and skin detection, demonstrate the usefulness of nonparametric Dirichlet mixtures in practice.

Understanding molecular structure, dynamics, and reactivity requires bridging processes that occur across widely separated time scales. Conventional molecular dynamics simulations provide atomistic resolution, but their femtosecond time steps limit access to the slow conformational changes and relaxation processes that govern chemical function. Here, we introduce a deep generative modeling framework that accelerates sampling of molecular dynamics by four orders of magnitude while retaining physical realism. Applied to small organic molecules and peptides, the approach enables quantitative characterization of equilibrium ensembles and dynamical relaxation processes that were previously only accessible by costly brute-force simulation. Importantly, the method generalizes across chemical composition and system size, extrapolating to peptides larger than those used for training, and captures chemically meaningful transitions on extended time scales. By expanding the accessible range of molecular motions without sacrificing atomistic detail, this approach opens new opportunities for probing conformational landscapes, thermodynamics, and kinetics in systems central to chemistry and biophysics.

We propose an ARIMA-TX-GARCH model and use it to forecast European Carbon Emission Allowance futures prices, incorporating Brent crude oil futures prices as an exogenous variable.

A long-standing gap exists between the theoretical analysis of Markov chain Monte Carlo convergence, which is often based on statistical divergences, and the diagnostics used in practice. We introduce the first general convergence diagnostics for Markov chain Monte Carlo based on any $f$-divergence, allowing users to directly monitor, among others, the Kullback-Leibler and the $\chi^2$ divergences as well as the Hellinger and the total variation distances. Our approach rests on a coupling-based "weight harmonization" scheme that produces direct, computable, and consistent importance weights for interacting Markov chains with respect to their target distribution. Beyond their use as convergence diagnostics, these weights are consistent estimates of the Radon-Nikodym derivative $\mathrm{d}\pi/\mathrm{d} \mu_t$, a richer object than the convergence bounds alone, with natural applications to importance-weighted inference. We show how such weightings can provide upper bounds to any $f$-divergence, prove that these bounds tighten over time and converge to zero as the chains approach stationarity, and demonstrate that, while more conservative than existing coupling-based total variation estimators, our method remains a practical and broadly applicable diagnostic tool.

Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero structure generalizes diagonality. These models have been the subject of recent work in non-independent component analysis. We show that pairwise mean independence answers the question of how much one can relax independence: it is identifiable, any weaker notion is non-identifiable, and it contains the models previously studied as special cases. Our results apply to distributions with the required zero pattern at any cumulant tensor. We propose an algebraic recovery algorithm based on least-squares optimization over the orthogonal group. Simulations highlight robustness: enforcing full independence can harm estimation, while pairwise mean independence enables more stable recovery. These findings extend the classical ICA framework and provide a rigorous basis for blind source separation beyond independence.

Smart surveys are surveys that make use of sensors and machine intelligence to reduce respondent burden and increase data quality. Smart surveys have been tests as a way to improve diary surveys in official statistics, where data are collected on topics such as travel, time use and household expenditures. There are often inherent differences both in measurement and representation between smart surveys and traditional diaries, which makes it difficult to integrate both data sources in producing statistics over time, or within a mixed- or multi-source context. This paper distinguishes two different approaches to integration: the mixed-mode approach, which prioritizes outcome alignment and minimizes measurement differences for straightforward data merging, and the multisource approach, which maintains inherent mode differences and integrates data at the modeling stage, allowing exploitation of the strengths of each source. Using travel surveys as an illustrative example, we explore the benefits and drawbacks of each approach, and propose a decision framework to guide researchers in selecting the appropriate integration strategy.

Understanding the association between dietary patterns and health outcomes, such as the cancer risk, is crucial to inform public health guidelines and shaping future dietary interventions. However, dietary intake data present several statistical challenges: they are high-dimensional, often sparse with excess zeros, and exhibit heterogeneity driven by individual-level covariates. Non-Negative Matrix Factorization (NMF), commonly used to estimate patterns in high-dimensional count data, typically relies on Poisson assumptions and lacks the flexibility to fully address these complexities. Additionally, integrating data across multiple studies, such as case-control studies on cancer risk, requires models that can share information across sources while preserving study-specific structure. In this paper, we introduce a novel Bayesian NMF model that (i) jointly models multi-study count data to enable cross-study information sharing, (ii) incorporate a mixture component to account for zero inflation, and (iii) leverage flexible Bayesian non-parametric priors for characterizing the heterogeneity in pattern scores induced by the individual covariates. This structure allows for clustering of individuals based on dietary profiles, enabling downstream association analyses with health outcomes. Through extensive simulation studies, we demonstrate that our model significantly improves estimation accuracy compared to existing Bayesian NMF methods. We further illustrate its utility through an application to multiple case-control studies on diet and upper aero-digestive tract cancers, identifying nutritionally meaningful dietary patterns. An R package implementing our approach is available at https://github.com/blhansen/ZIMultiStudyNMF.

Truncation by death, a prevalent challenge in critical care, renders traditional dynamic treatment regime (DTR) evaluation inapplicable due to ill-defined potential outcomes. We introduce a principal stratification-based method, focusing on the always-survivor value function. We derive a semiparametrically efficient, multiply robust estimator for multi-stage DTRs, demonstrating its robustness and efficiency. Empirical validation and an application to electronic health records showcase its utility for personalized treatment optimization.

Hierarchical data with multiple observations per group is ubiquitous in empirical sciences and is often analyzed using mixed-effects regression. In such models, Bayesian inference gives an estimate of uncertainty but is analytically intractable and requires costly approximation using Markov Chain Monte Carlo (MCMC) methods. Neural posterior estimation shifts the bulk of computation from inference time to pre-training time, amortizing over simulated datasets with known ground truth targets. We propose metabeta, a neural network model for Bayesian mixed-effects regression. Using simulated and real data, we show that it reaches stable and comparable performance to MCMC-based parameter estimation at a fraction of the usually required time, enabling new use cases for Bayesian mixed-effects modeling.

GPU kernel generation by LLMs has recently experienced rapid development, leveraging test-time scaling and reinforcement learning techniques. However, a key challenge for kernel generation is the scarcity of high-quality data, as most high-quality kernels are proprietary and not open-source. This challenge prevents us from leveraging supervised fine-tuning to align LLMs to the kernel generation task. To address this challenge, we develop a pipeline that generates and curates high-quality CUDA kernels with reasoning traces, motivated by a critical observation that concise yet informative reasoning traces result in robust generation of high-performance kernels. Using this pipeline, we construct our dataset ConCuR and introduce our model KernelCoder, which is the first model trained on a curated dataset consisting of PyTorch, reasoning, and CUDA kernel pairs, to our knowledge. In the KernelBench setup, our model achieves significant improvements over the existing top-performing model, QwQ-32B, and outperforms all open-source models fine-tuned for kernel generation, as well as frontier models such as DeepSeek-V3.1-Think and Claude-4-sonnet. Finally, we show that the average reasoning length can serve as a metric to assess the difficulty of kernel generation tasks. The observations, metrics, and our data collection and curation pipeline can help obtain better data in the kernel generation task in the future.

Road traffic accidents remain a major public health challenge worldwide, with urbanisation and population density identified as key factors influencing risk. This study analyses monthly accident data from 2009 to 2023 across 632 parliamentary constituencies in England, Wales, and Scotland, using an area-normalised approach based on population density. Segmented power law models consistently identified breakpoints separating sublinear rural from superlinear urban scaling behaviours. Seasonal variation in scaling exponents was pronounced in rural regions but less evident in urban ones. Fourier-based cross-spectral analysis of yearly cycles revealed systematic phase shifts: rural exponents lagged pre-exponential factors by 4.5 months, while urban exponents were 2.7 months out of phase, producing a 5.3 month shift between rural and urban exponents. These findings highlight the importance of pre-exponentials-defined as the expected density of accidents at unit population density-as comparable descaled metrics, revealing both long-term national declines and recurring seasonal peaks. Notably, the phase offsets suggest structurally distinct causes of rural and urban accident risk, with urban regions exhibiting increasing acceleration in accident scaling, potentially linked to growth in vehicle numbers, size, and weight. Residuals, modelled with the Type I Generalised Logistic Distribution (GLD), captured skewness and heterogeneity more effectively than normal assumptions. Geospatial mapping highlighted persistent urban hotspots alongside rural and coastal constituencies with systematically lower accident densities than predicted. Together, these findings advance understanding of how density and urbanisation shape accident risk and provide evidence to support more targeted road safety interventions and policy planning.

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to viable fusion power is understanding plasma turbulence, which significantly impairs plasma confinement, and is vital for next-generation reactor design. Plasma turbulence is governed by the nonlinear gyrokinetic equation, which evolves a 5D distribution function over time. Due to its high computational cost, reduced-order models are often employed in practice to approximate turbulent transport of energy. However, they omit nonlinear effects unique to the full 5D dynamics. To tackle this, we introduce GyroSwin, the first scalable 5D neural surrogate that can model 5D nonlinear gyrokinetic simulations, thereby capturing the physical phenomena neglected by reduced models, while providing accurate estimates of turbulent heat transport. GyroSwin (i) extends hierarchical Vision Transformers to 5D, (ii) introduces cross-attention and integration modules for latent 3D$\leftrightarrow$5D interactions between electrostatic potential fields and the distribution function, and (iii) performs channelwise mode separation inspired by nonlinear physics. We demonstrate that GyroSwin outperforms widely used reduced numerics on heat flux prediction, captures the turbulent energy cascade, and reduces the cost of fully resolved nonlinear gyrokinetics by three orders of magnitude while remaining physically verifiable. GyroSwin shows promising scaling laws, tested up to one billion parameters, paving the way for scalable neural surrogates for gyrokinetic simulations of plasma turbulence.

This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. Limits for the empirical spectral distributions of its two symmetrized versions are established in the proportional high-dimensional regime, one of them being the semicircle law, thereby giving a first example of a correlation matrix with a non-Marchenko–Pastur spectral limit, in contrast to the Pearson, Kendall, and Spearman cases. We further establish central limit theorems for linear spectral statistics of the symmetrized matrices. As an important application of this theory, we develop Chatterjee's rank correlation-based tests for the complete independence among the components.

Given a single observation from a Gaussian distribution with unknown mean $\theta$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_{\theta}$ uniformly for all $\theta$ in a parameter set. We leverage our technique to establish reduction-based computational lower bounds for several canonical high-dimensional statistical models under widely-believed conjectures in average-case complexity. In particular, we cover cases in which: 1. $Q_{\theta}$ is a general location model with non-Gaussian distribution, including both light-tailed examples (e.g., generalized normal distributions) and heavy-tailed ones (e.g., Student's $t$-distributions). As a consequence, we show that computational lower bounds proved for spiked tensor PCA with Gaussian noise are universal, in that they extend to other non-Gaussian noise distributions within our class. 2. $Q_{\theta}$ is a normal distribution with mean $f(\theta)$ for a general, smooth, and nonlinear link function $f:\mathbb{R} \rightarrow \mathbb{R}$. Using this reduction, we construct a reduction from symmetric mixtures of linear regressions to generalized linear models with link function $f$, and establish computational lower bounds for solving the $k$-sparse generalized linear model when $f$ is an even function. This result constitutes the first reduction-based confirmation of a $k$-to-$k^2$ statistical-to-computational gap in $k$-sparse phase retrieval, resolving a conjecture posed by Cai et al. (2016). As a second application, we construct a reduction from the sparse rank-1 submatrix model to the planted submatrix model, establishing a pointwise correspondence between the phase diagrams of the two models that faithfully preserves regions of computational hardness and tractability.

We study nonparametric estimation of univariate cumulative distribution functions (CDFs) pertaining to data missing at random. The proposed estimators smooth the inverse probability weighted (IPW) empirical CDF with the Bernstein operator, yielding monotone, $[0,1]$-valued curves that automatically adapt to bounded supports. We analyze two versions: a pseudo estimator that uses known propensities and a feasible estimator that uses propensities estimated nonparametrically from discrete auxiliary variables, the latter scenario being much more common in practice. For both, we derive pointwise bias and variance expansions, establish the optimal polynomial degree $m$ with respect to the mean integrated squared error, and prove the asymptotic normality. A key finding is that the feasible estimator has a smaller variance than the pseudo estimator by an explicit nonnegative correction term. We also develop an efficient degree selection procedure via least-squares cross-validation. Monte Carlo experiments show that, for small to moderate sample sizes, the Bernstein-smoothed pseudo and feasible estimators outperform their unsmoothed counterparts and the integrated version of the IPW kernel density estimator proposed by Dubnicka (2009), under certain models. A real-data application to fasting plasma glucose from the 2017-2018 NHANES survey illustrates the method in a practical setting. All code needed to reproduce our analyses is readily accessible on GitHub.

This paper derives new asymptotic results for the adaptive LASSO estimator in cointegrating regressions, allowing for uncertainty about whether the regressors are exact unit root processes. We study model selection probabilities, estimator consistency, and limiting distributions under standard and moving-parameter asymptotics. We further derive uniform convergence rates and the fastest local-to-zero rates detectable by the estimator under conservative and consistent tuning. For consistent tuning, we construct confidence regions that are easy to implement, uniformly valid over the parameter space, and achieve sure asymptotic coverage without requiring knowledge or estimation of local-to-unity or long-run covariance parameters. Simulation results reveal that the finite-sample distribution of the adaptive LASSO estimator can deviate substantially from the oracle property, whereas moving-parameter asymptotics provide much more accurate approximations. Consequently, in addition to being infeasible in applications due to their dependence on non-estimable nuisance parameters, oracle-based confidence regions are often too small to achieve adequate coverage in empirically relevant scenarios with small but non-zero coefficients. In contrast, the proposed confidence regions are always feasible and deliver reliable coverage across the parameter space. An empirical application to predicting the U.S. unemployment rate illustrates their practical usefulness for quantifying uncertainty around adaptive LASSO estimates.

The spatial-temporal imbalance between supply and demand in shared micro-mobility services often leads to observed demand being censored, resulting in incomplete records of the underlying real demand. This phenomenon undermines the reliability of the collected demand data and hampers downstream applications such as demand forecasting, fleet management, and micro-mobility planning. How to accurately estimate the real demand is challenging and has not been well explored in existing studies. In view of this, we contribute to real demand estimation for shared micro-mobility services by proposing an analytical method that rigorously derives the real demand under appropriate assumptions. Rather than directly modeling the intractable relationship between observed demand and real demand, we propose a novel random variable, Generalized Vehicle Survival Time (GVST), which is observable from trip records. The relationship between GVST and real demand is characterized by introducing a flipped queueing model (FQM) that captures the operational dynamics of shared micro-mobility services. Specifically, the distribution of GVST is derived within the FQM, which allows the real demand estimation problem to be transformed into an inverse queueing problem. We analytically derive the real demand in closed form using a one-sided estimation method, and solve the problem by a system of equations in a two-sided estimation method. We validate the proposed methods using synthetic data and conduct empirical analyses using real-world datasets from bike-sharing and shared e-scooter systems. The experimental results show that both the two-sided and one-sided methods outperform benchmark models. In particular, the one-sided approach provides a closed-form solution that delivers acceptable accuracy, constituting a practical rule of thumb for demand-related analytics and decision-making processes.

Methods for split conformal prediction leverage calibration samples to transform any prediction rule into a set-prediction rule that complies with a target coverage probability. Existing methods provide remarkably strong performance guarantees with minimal computational costs. However, they require to use calibration samples composed by labeled examples different to those used for training. This requirement can be highly inconvenient, as it prevents the use of all labeled examples for training and may require acquiring additional labels solely for calibration. This paper presents an effective methodology for split conformal prediction with unsupervised calibration for classification tasks. In the proposed approach, set-prediction rules are obtained using unsupervised calibration samples together with supervised training samples previously used to learn the classification rule. Theoretical and experimental results show that the presented methods can achieve performance comparable to that with supervised calibration, at the expenses of a moderate degradation in performance guarantees and computational efficiency.