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利用正则变差随机向量的凸组合估计谱测度AI 解读

The extremal dependence structure of a regularly varying random vector X is fully described by its limiting spectral measure. In this paper, we investigate how to recover characteristics of the measure, such as extremal coefficients, from the extremal behaviour of convex combinations of components of X. Our considerations result in a class of new estimators of moments of the corresponding combinations for the spectral vector. We show asymptotic normality by means of a…

非独立成分分析AI 解读

A seminal result in the ICA literature states that for AY=ε, if the components of ε are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows (Signal Process. 36 (1994)). In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of ε. We document new conditions that establish identification for several nonindependent component…

通过树计数高效检验网络相关性AI 解读

We propose a new procedure for testing whether two networks are edge-correlated through some latent vertex correspondence. The test statistic is based on counting the cooccurrences of signed trees for a family of nonisomorphic trees. When the two networks are Erdős–Rényi random graphs G(n,q) that are either independent or correlated with correlation coefficient ρ, our test runs in n2+o(1) time and succeeds with high probability as n→∞, provided that nmin{q,1−q}≥n−o(1) and…

投资型资产定价模型的估计与检验AI 解读

Investment-based asset pricing models typically predict a close link between a firm’s stock return and its characteristics at any point in time. Yet, previous studies have primarily focused on the weaker prediction that this link holds on average, finding substantial empirical support. We show how to incorporate the time-series predictions in the estimation and testing of investment-based models using the generalized method of moments. We find that standard specifications of…

个人税收是否影响投资决策与股票收益？AI 解读

This paper studies the causal effects of personal investment taxes on stock returns and the financial decisions of companies. I exploit a change in legislation in 2013 which allowed stocks listed on the Alternative Investment Market, a sub-market of the London Stock Exchange, to be held in capital gains and dividend tax-exempt investment accounts for the first time. Using a difference-in-differences approach, I find that excess stock returns decreased by their…

缺乏小阶有限矩的 GARCH-MIDAS 模型推断AI 解读

In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown…

预测回归的新稳健推断方法AI 解读

We propose a robust inference method for predictive regression models under heterogeneously persistent volatility as well as endogeneity, persistence, or heavy-tailedness of regressors. This approach relies on two methodologies, nonlinear instrumental variable estimation and volatility correction, which are used to deal with the aforementioned characteristics of regressors and volatility, respectively. Our method is simple to implement and is applicable both in the case of…

含交互固定效应的核范数正则化分位数回归AI 解读

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T . We derive an error…

非线性选择模型中的截距估计AI 解读

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then…

含协变量的分布泛函序贯处理分配AI 解读

We consider a sequential treatment problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision-maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socioeconomic functional such as an inequality, welfare, or poverty measure. We develop expected regret lower bounds for…

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…