order statistics

This paper addresses the critical problem of variance reduction via stratified sampling in online A/B testing. We propose an efficient stratification variable subset selection algorithm that dynamically evaluates the marginal contribution of each variable to estimation variance through layer-wise simulation of the stratification process, enabling precise identification of high-information stratification variables—even under multivariate correlation. Unlike conventional approaches relying on pairwise correlation or heuristic filtering, our method directly optimizes for variance minimization, ensuring both theoretical interpretability and computational efficiency. Experiments on synthetic and real-world business datasets demonstrate that our approach reduces estimation variance by 18%–32% on average compared to classical methods such as covariate adjustment and CUPED. This translates into significantly improved statistical power and experimental sensitivity, facilitating faster and more reliable causal inference in production A/B testing environments.

In A/B testing, rigorously evaluating novel estimation algorithms—when the true treatment effect is unobserved—remains a fundamental methodological challenge. This paper establishes, for the first time, a comprehensive theoretical framework for estimation and inference based on sample splitting: it derives the asymptotic distribution of sample-split estimators and characterizes their bias structure relative to full-sample performance; introduces a bias–variance trade-off analytical paradigm and proposes a correction-based confidence interval construction method. Leveraging statistical inference, asymptotic theory, Monte Carlo simulation, and empirical validation, the framework enables robust, production-grade evaluation of new algorithms within industrial A/B testing platforms. Theoretical results are thoroughly validated via simulation studies. The proposed infrastructure enhances A/B testing methodology by delivering an interpretable, reproducible, and deployable evaluation system.

This study addresses severe congestion in the interview stage of academic statistics faculty hiring, which obscures candidates’ true preferences and leads to mismatches and unfilled positions. The authors model interview assignment as a statistical ranking problem under uncertainty, innovatively integrating market design with statistical learning. Candidates report their preferences over job attributes via a standardized questionnaire, while departments estimate offer probabilities and expected utilities using application materials and historical data. A confidence-calibrated pairwise utility ranking mechanism is then employed to select interviewees. This mechanism provides statistical guarantees, incentivizes truthful preference revelation, and enhances matching stability. Empirical evaluation using data from U.S. statistics departments demonstrates that the proposed framework substantially improves both match rates and quality while significantly reducing hiring failure rates.

In resource-constrained multiple testing, exhaustive evaluation of all hypotheses and computation of exact test statistics (e.g., via experiments or precise calculations) is infeasible. Method: This paper proposes a surrogate-driven active testing framework that leverages auxiliary information—such as expert judgment, ML predictions, or historical data—to construct surrogate test statistics. It dynamically decides whether to invoke costly exact tests; otherwise, it substitutes the surrogate values directly. Contribution/Results: The framework is the first to enable compatible p-value and e-value constructions under arbitrary dependence structures—without requiring independence between surrogates and true statistics—while provably controlling the false discovery rate (FDR). By unifying active learning, multiple testing theory, and e-value theory, it achieves both theoretical rigor and practical utility. Empirical evaluation on scCRISPR causal effect analysis demonstrates a 32% increase in discoveries and a 68% reduction in computational cost compared to exhaustive testing, under identical FDR constraints.

This paper addresses the nonparametric sequential two-sample testing problem by proposing a novel, consistent testing framework grounded in the “testing-by-betting” paradigm. The method models statistical testing as a gambler’s wealth-maximization process over sequential observations, with cumulative wealth serving as the evidence against the null hypothesis. Crucially, it establishes the first deep integration of test martingales with regret analysis of online prediction strategies—enabling validity under nonexchangeable sequences, general invariances (e.g., symmetry, independence), and adaptive difficulty settings. Theoretically, the test is proven to be consistent, achieves the optimal exponential convergence rate for Type-II error, and admits a finite upper bound on expected sample size. Empirical evaluations demonstrate strong adaptivity to the unknown complexity of alternative distributions, substantially outperforming existing sequential two-sample tests.

This study addresses the lack of rigorous statistical assessment for the reliability of output structures in complex clustering pipelines that involve multiple data-dependent stages such as anomaly detection, feature selection, and clustering. To bridge this gap, the work systematically applies selective inference to the entire clustering analysis workflow, establishing a statistical framework that enables valid significance testing of final cluster assignments. The proposed method rigorously controls the type I error rate at any pre-specified nominal level and demonstrates strong empirical performance on both synthetic and real-world datasets. By doing so, it provides a principled and reliable foundation for statistical inference in multi-stage, data-driven clustering procedures.

This paper addresses the statistical analysis challenge of set-valued data (e.g., EMI injection point sets from electronic devices) in inter-laboratory comparisons. Methodologically, it proposes a consensus inference–oriented modeling framework that innovatively integrates Hamming distance to quantify set dissimilarity, Fisher’s noncentral hypergeometric distribution to model deviation counts, and a Bayesian hierarchical model to disentangle inter-laboratory consensus from intra-laboratory variability. Key contributions include: (i) the first application of the noncentral hypergeometric distribution to set-based consensus modeling, enabling statistically rigorous quantification of deviation counts; (ii) simultaneous estimation of a global consensus set and laboratory-specific offsets via hierarchical Bayesian inference; and (iii) substantially improved comparability and reliability of multi-laboratory results. The method is validated on real-world EMC inter-comparison data, demonstrating its effectiveness in identifying robust consensus sets and quantifying intra-laboratory variation.

This study addresses the fundamental question of whether a statistical parameter defined through a conditional distribution remains constant across covariates—a problem encompassing treatment effect heterogeneity and conditional association. The authors propose a general nonparametric testing framework based on smooth functionals applied to conditional distributions, yielding functional parameters for which they construct test statistics with tractable asymptotic distributions. Their approach explicitly links to norm-based tests in function spaces and, compared to existing norm-type methods, exhibits superior asymptotic properties under the null hypothesis. Simulation studies demonstrate strong finite-sample performance, and the method is successfully applied to data from a breast cancer clinical trial, effectively identifying key biomarkers predictive of response to adjuvant chemotherapy.

This paper addresses the active nonparametric sequential two-sample test problem under multi-source heterogeneous data, aiming to determine whether paired samples originate from the same unknown distribution with minimal expected sampling cost. We propose the first method integrating active learning with the “testing-by-betting” framework: a nonnegative martingale-based betting wealth process is designed; an empirically measurable distinguishability criterion guides source selection; and a vanishing greedy exploration mechanism balances exploration and exploitation. Under no distributional assumptions, the method strictly controls Type-I error at level α and achieves power-one under the alternative. A theoretical upper bound on the expected stopping time is derived, substantially improving upon passive sampling baselines. The core contribution is the first statistically rigorous and sample-efficient active sequential testing paradigm for multi-source nonparametric two-sample testing.

This study addresses the challenge of coarsened data arising in two-stage sampling when only a subset of variables is observed in the second stage. Under the assumption that the outcome variable is fully observed, the authors propose a class of novel estimators based on targeted maximum likelihood estimation (TMLE). This approach provides a unified framework for modeling the second-stage sampling mechanism, encompassing generalized calibration estimation, inverse probability of censoring weighted TMLE (IPCW-TMLE), and their extensions. The proposed estimators possess double robustness and achieve higher efficiency, with theoretical analysis demonstrating that they attain the semiparametric efficiency bound asymptotically—matching the best-known performance in the literature—and thereby substantially improving the precision of parameter estimation.