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Wenkai Xu 对《安全检验》的讨论AI 解读

The authors propose the framework of e-value testing by investigating the grow-rate-optimal (GRO) constructions of e-variables, that incorporate a comprehensive range of testing scenarios for simple alternative, as well as their composite counterparts. The authors illustrate the versatility of e-value tests via three interpretations, drawing connections to (1) game-theoretical viewpoint, (2) conservative p-values, and (3) Bayes Factors; and devise the determination and…

Judith ter Schure 对《安全检验》的讨论AI 解读

Once there was a randomized controlled trial (RCT) that studied the recurrence of stroke. It had assumed for the treatment of interest a 40% reduction in hazard, and had set the sample size accordingly (Kamel et al., 2024). The RCT found a 95% confidence interval of (−55%, 36%) and concluded no statistical significance. ‘Absence of evidence is not evidence of absence’ said the statisticians (Altman & Bland, 1995; Harrell, 2024). But the story goes that the sample size was…

Pace 与 Salvan 对《安全检验》的讨论贡献AI 解读

We wish to congratulate the authors on their important paper. In this contribution, we will focus on parametric models, where e-values provide a welcome new perspective on likelihood ratios and Bayes factors, as well as a useful addition to the discussion about the foundational concept of statistical evidence. The guarantees sought for in safe testing are frequentist, but prior information may be injected in Bayesian terms, establishing an alliance between traditionally…

Christine P. Chai 对《安全检验》的讨论AI 解读

This paper proposes the e-value for ‘safe testing’ as an alternative to the p-value in hypothesis testing. The e-value allows for optional continuation while preserving Type-I error guarantees. I hope to see lots of discussion at the Royal Statistical Society meeting, like the previous ‘Signs and sizes: Understanding and replicating statistical findings’ (Hutton et al., 2020). I have some questions regarding the descriptions: I see some comparisons between the e-value and…

田茂再、余克明与王江峰对《安全检验》的讨论AI 解读

We want to congratulate the authors on the publication of ‘Safe Testing’ on JRSS-B. It deepens our understanding of the statistical hypothesis test that is one particular method of statistical inference used to decide whether the data sufficiently support a particular hypothesis. The e-variables and safe tests offer several advantages. The authors develop the theory of hypothesis testing based on the e-value that behave excellently under optional continuation and are…

Joris Mulder 对《安全检验》的讨论评论AI 解读

The potential of e-values (or e-variables) to unite different schools of statistics and allowing optional stopping/continuation in a ‘safe’ manner is a major accomplishment of the authors. The theory implies a change in focus from classical error rates to the expected evidence against the null under the respective hypotheses. Under H0⁠, it is required that the expectation of the evidence against the null, E, should not exceed 1, i.e. EH0[E]≤1⁠, as in formula (1) of ‘Safe…

Christian Hennig对《安全检验》的讨论AI 解读

I appreciate the elegance of the theory regarding (RE)GRO(W) e-variables with optional continuation for combining evidence. Here are some rather problematic aspects. (1) The authors state that ‘there seems to be growing consensus that, in the context of hypothesis testing, p-values should either not be used at all, or at least, with utter care’. I see little consensus that p-values should not be used at all. The request for ‘utter care’ is sensible, but I do not believe that…

Alexander Ly对《安全检验》的讨论意见AI 解读

The article by Grünwald, de Heide, and Koolen not only presents a comprehensive approach to anytime-valid testing but also offers profound insights and inspiration for statistical practice. However, there is a potential inconvenience in cases where achieving gro(w) optimality necessitates the use of point priors. In these instances, the specified point of the point prior never vanishes from the associated anytime-valid confidence interval, and it prohibits powerful…

Robert 与 Bon 对《安全检验》的讨论意见AI 解读

Central to our interest in Bayesian foundations and reference priors, the connection made in this paper between e-values and Bayes factors, despite the cautionary added label of an ‘Almost Bayesian Case’, could bring a formal way to define least favourable priors (Berger, 1985) in a testing environment, albeit in no clear connection with the reference priors of Bayarri and Garcia-Donato (2007). This derivation, formalized as Theorem 1, provides a reversal of the typical…

Joshua Bon与Christian P. Robert对《安全检验》的讨论AI 解读

The central proposal found in this quite original paper could prove relevant for the so-called objective Bayes approach (Berger, 1985; Robert, 2001) as it may open a way to deriving prior distributions from (frequentist) first principles. While some Bayesian schools refuse to consider the concept of testing the veracity of a null hypothesis, most do propose approaches and methodologies to address this challenge. These mainly rely on Jeffreys’ formalization via two prior…

Vladimir Vovk 对《安全检验》的讨论意见AI 解读

The main result of this paper (Theorem 1) is elegant and satisfying, but in this comment I will concentrate on one of its limitations, namely the condition infW0D(Q‖PW0)<∞⁠. (Analogous conditions are present in all generalizations given in the paper.) Even in the toy binary case with an infinite horizon, this condition is typically violated. Consider, e.g., the case of Markov alternative hypotheses Q considered in Ramdas et al. (2022): a nonIID Markov probability measure (or…

Dey、Martin 与 Williams 对《安全检验》的讨论贡献AI 解读

Congratulations to Grünwald, de Heide, and Koolen (GHK) for their contribution to the exciting and rapidly growing literature on safe/anytime-valid inference. GHK’s proposal focused on problems in which a statistical model is available that determines the quantity of interest—the model parameter—and provides a likelihood function that drives the e-value construction. When data are observed and analysed sequentially, however, the data analyst typically cannot say with any…

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…

相关性调整的去偏 Lasso：协变量模型不准确时的去偏AI 解读

Abstract We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical inference. Several authors suggest to orthogonalize both the variable of interest and the outcome with respect to the nuisance variables, and then regress the residual outcome with respect to the residual variable. This is possible if the…

神经网络与随机森林的融合AI 解读

Abstract Neural networks and random forests are popular and promising tools for machine learning. This article explores the proper integration of these two approaches for nonparametric regression to improve the performance of a single approach. Specifically, we propose a neural network estimator with local enhancement provided by random forests. It naturally synthesizes the local relation adaptivity of random forests and the strong global approximation ability of neural…

动态张量的 CP 因子模型AI 解读

Abstract Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly…

处理依赖性右删失的近端生存分析AI 解读

Abstract Many epidemiological and clinical studies aim to analyse a time-to-event endpoint. A common complication is right censoring. In some cases, right censoring occurs when subjects are still surviving after the study terminates or move out of the study area. In such cases, right censoring is typically treated as independent or noninformative. This assumption can be further relaxed to conditional independent censoring by leveraging possibly time-varying covariate…

分组数据部分线性模型中提高估计精度的夹心提升法AI 解读

Abstract We study partially linear models in settings where observations are arranged in independent groups but may exhibit within-group dependence. Existing approaches estimate linear model parameters through weighted least squares, with optimal weights (given by the inverse covariance of the response, conditional on the covariates) typically estimated by maximizing a (restricted) likelihood from random effects modelling or by using generalized estimating equations. We…

未观测混杂下处理效应的模型辅助敏感性分析：正则化校准估计AI 解读

Abstract Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model. At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions. We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression. At the sample level, we develop new methods and theory for obtaining not only doubly…

基于测度运输的方向数据非参数方法AI 解读

Abstract This article proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile contours and regions and closed-form formulas under the classical assumption of rotational symmetry. The empirical versions of our distribution functions enjoy the expected Glivenko–Cantelli property of traditional distribution…

Green 匹配：复杂动力系统参数估计的高效方法AI 解读

Abstract Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green’s matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate…

匹配设计中的协变量自适应随机化推断AI 解读

Abstract It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This approach ignores observed discrepancies in matched sets that may be consequential for the distribution of treatment, which are succinctly captured by within-set differences in the propensity score. We address this problem via…

高斯图模型的极小极大检测边界与精确最优检验AI 解读

Abstract In this article, we derive the minimax detection boundary for testing a sub-block of variables in a precision matrix under the Gaussian distribution. Compared to the results on the minimum rate of signals for testing precision matrices in literature, our result gives the exact minimum signal strength in a precision matrix that can be detected. We propose a thresholding test that is able to achieve the minimax detection boundary under certain cases by adaptively…

广播式非参数张量回归AI 解读

Abstract We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate. We also provide a minimax lower…