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跨滤过的信息证据合并AI 解读

Abstract In sequential anytime-valid inference, any admissible procedure must be based on e-processes: generalizations of test martingales that quantify the accumulated evidence against a composite null hypothesis at any stopping time. This paper proposes a method for combining e-processes constructed in different filtrations but for the same null. Although e-processes in the same filtration can be combined effortlessly (by averaging), e-processes in different filtrations…

序贯变点定位的检测后推断AI 解读

Abstract This article addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown changepoint using only the data observed up to a data-dependent stopping time at which an arbitrary sequential detection algorithm declares a change. Our framework is nonparametric, making no assumption on the composite postchange…

通过下注构造序贯蒙特卡洛检验AI 解读

Abstract In a Monte Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones. Sequential Monte Carlo tests aim to save computational resources by generating these additional datasets sequentially one by one and potentially stopping early. While earlier tests yield valid inference at a particular prespecified…

数据裂分：拆分单个数据点AI 解读

Suppose we observe a random vector X from some distribution in a known family with unknown parameters. We ask the following question: when is it possible to split X into two pieces f(X) and g(X) such that neither part is sufficient to reconstruct X by itself, but both together can recover X fully, and their joint distribution is tractable? One common solution to this problem when multiple samples of X are observed is data splitting, but Rasines and Young offers an…

时间一致中心极限定理与渐近置信序列AI 解读

Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals, adding to the literature on confidence sequences (CS)—sequences of…

Larsson、Ramdas 与 Ruf 对《安全检验》的讨论AI 解读

We congratulate the authors on a stimulating article that has inspired many follow-up works. We discuss the central concept of growth-rate optimality (GRO). For a point null and alternative, the GRO e-variable is their likelihood ratio (Shafer, 2021). The generalization to composite nulls takes centre stage in Grünwald et al. (2024). Their use of the reverse information projection (RIPr) builds on Li (1999), and has been recently extended in Lardy et al. (2023). Inspired by…

复合假设下有检验能力的p值与e值的存在性AI 解读

Given a composite null P and composite alternative Q, when and how can we construct a p-value whose distribution is exactly uniform under the null, and stochastically smaller than uniform under the alternative? Similarly, when and how can we construct an e-value whose expectation exactly equals one under the null, but its expected logarithm under the alternative is positive? We answer these basic questions, and other related ones, when P and Q are convex polytopes (in the…

摘要暂缺

Abstract We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form "betting" CSs and CIs. Our method combines new composite nonnegative (super)martingales with Ville's maximal inequality, with…

双层层级模型的分布无关预测集AI 解读

We consider the problem of constructing distribution-free prediction sets for data from two-layer hierarchical distributions. For iid data, prediction sets can be constructed using the method of conformal prediction. The validity of conformal prediction hinges on the exchangeability of the data, which does not hold when groups of observations come from distinct distributions, such as multiple observations on each patient in a medical database. We extend conformal methods to…

高斯模型中的通用似然比检验AI 解读

Summary The classical likelihood ratio test based on the asymptotic chi-squared distribution of the log-likelihood is one of the fundamental tools of statistical inference. A recent universal likelihood ratio test approach based on sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute the split likelihood ratio statistic, or, more generally, an upper bound on the null maximum likelihood. The universal likelihood ratio…

使用 e 值控制错误发现率AI 解读

Abstract E-values have gained attention as potential alternatives to p-values as measures of uncertainty, significance and evidence. In brief, e-values are realized by random variables with expectation at most one under the null; examples include betting scores, (point null) Bayes factors, likelihood ratios and stopped supermartingales. We design a natural analogue of the Benjamini-Hochberg (BH) procedure for false discovery rate (FDR) control that utilizes e-values, called…

通过蒸馏实现快速且有力的条件随机化检验AI 解读

Summary We consider the problem of conditional independence testing: given a response $Y$ and covariates $(X,Z)$, we test the null hypothesis that $Y {\perp\!\!\!\perp} X \mid Z$. The conditional randomization test was recently proposed as a way to use distributional information about $X\mid Z$ to exactly and nonasymptotically control Type-I error using any test statistic in any dimensionality without assuming anything about $Y\mid (X,Z)$. This flexibility, in principle,…

结构约束下控制错误发现率的一般交互框架AI 解读

Summary We propose a general framework based on selectively traversed accumulation rules for interactive multiple testing with generic structural constraints on the rejection set. It combines accumulation tests from ordered multiple testing with data-carving ideas from post-selection inference, allowing highly flexible adaptation to generic structural information. Our procedure defines an interactive protocol for gradually pruning a candidate rejection set, beginning with…

时间一致、非参数、非渐近的置信序列AI 解读

A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric conditions. We draw connections between the Cramér–Chernoff method for exponential concentration, the law of the iterated logarithm (LIL) and the sequential probability ratio test—our confidence sequences are time-uniform extensions of the…

以分类准确率作为两样本检验的替代依据AI 解读

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the high-dimensional setting. We prove two results that hold for all classifiers in any dimensions: if its true error remains $\epsilon $-better than chance for some $\epsilon >0$ as $d,n\to \infty $, then (a) the permutation-based test is consistent…

使用 jackknife+ 的预测推断AI 解读

This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we…

结构化、回归及在线场景中错误发现比例的同时高概率界AI 解读

While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (Statist. Sci. 26 (2011) 584–597) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set. In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets. While most existing simultaneous…

有向无环图上控制错误发现率的序贯算法AI 解读

We propose a linear-time, single-pass, top-down algorithm for multiple testing on directed acyclic graphs, where nodes represent hypotheses and edges specify a partial ordering in which the hypotheses must be tested. The procedure is guaranteed to reject a sub-directed acyclic graph with bounded false discovery rate while satisfying the logical constraint that a rejected node’s parents must also be rejected. It is designed for sequential testing settings where the directed…

p-filter：分组假设的多层错误发现率控制AI 解读

Summary In many practical applications of multiple testing, there are natural ways to partition the hypotheses into groups by using the structural, spatial or temporal relatedness of the hypotheses, and this prior knowledge is not used in the classical Benjamini–Hochberg procedure for controlling the false discovery rate (FDR). When one can define (possibly several) such partitions, it may be desirable to control the group FDR simultaneously for all partitions (as special…