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关于 e 值与多重检验的一则研究AI 解读

Summary We discover a connection between the Benjamini–Hochberg procedure and the e-Benjamini–Hochberg procedure (Wang & Ramdas, 2022) with a suitably defined set of e-values. This insight extends to Storey’s procedure and generalized versions of the Benjamini–Hochberg procedure and the model-free multiple testing procedure of Barber & Candés (2015) with a general form of rejection rules. We further summarize these findings in a unified form. These connections open up new…

高维因子定价模型中 alpha 的自适应检验AI 解读

This article proposes a new procedure to validate the multi-factor pricing theory by testing the presence of alpha in linear factor pricing models with a large number of assets. Because the market’s inefficient pricing is likely to occur to a small fraction of exceptional assets, we develop a testing procedure that is particularly powerful against sparse signals. Based on the high-dimensional Gaussian approximation theory, we propose a simulation-based approach to…

多元线性回归中的高维方差分析AI 解读

Summary In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate…

高维核两样本检验：矩差异与维数、样本量阶数的相互作用AI 解读

Summary Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behaviour of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the maximum mean discrepancy using an isotropic kernel, which includes maximum mean discrepancy with the Gaussian kernel and the Laplace kernel, and the energy distance as special cases. We derive asymptotic expansions of the kernel…

利用辅助信息的大规模多重检验最优错误发现率控制AI 解读

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a…

协变量自适应的错误发现率控制及组学多重检验应用AI 解读

Conventional multiple testing procedures often assume hypotheses for different features are exchangeable. However, in many scientific applications, additional covariate information regarding the patterns of signals and nulls are available. In this article, we introduce an FDR control procedure in large-scale inference problem that can incorporate covariate information. We develop a fast algorithm to implement the proposed procedure and prove its asymptotic validity even when…

两个时空随机场空间特征局部差异的检测AI 解读

Comparing the spatial characteristics of spatiotemporal random fields is often at demand. However, the comparison can be challenging due to the high-dimensional feature and dependency in the data. We develop a new multiple testing approach to detect local differences in the spatial characteristics of two spatiotemporal random fields by taking the spatial information into account. Our method adopts a two-component mixture model for location wise p-values and then derives a…

全基因组关联研究中协变量自适应的族错误率控制AI 解读

Summary The familywise error rate has been widely used in genome-wide association studies. With the increasing availability of functional genomics data, it is possible to increase detection power by leveraging these genomic functional annotations. Previous efforts to accommodate covariates in multiple testing focused on false discovery rate control, while covariate-adaptive procedures controlling the familywise error rate remain underdeveloped. Here, we propose a novel…

高维情形下基于距离与再生核希尔伯特空间的依赖度量AI 解读

In this paper, we study distance covariance, Hilbert–Schmidt covariance (aka Hilbert–Schmidt independence criterion [In Advances in Neural Information Processing Systems (2008) 585–592]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert–Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates…

衡量联合依赖的距离度量及其在因果推断中的应用AI 解读

Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d≥2 random vectors. We introduce the high-order distance covariance to measure the so-called Lancaster interaction dependence. The joint distance covariance is then defined as a linear combination of pairwise distance covariances and their higher-order counterparts…

基于距离协方差的高维相互独立性检验AI 解读

Summary We introduce an L2-type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed on the basis of the pairwise distance covariance and it accounts for the non-linear and non-monotone dependences among the data, which cannot be fully captured by the existing tests based on either Pearson correlation or rank correlation. Our test can be conveniently implemented in practice as the limiting null distribution…

Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recently proposed in Shao and Zhang [J. Amer. Statist. Assoc. 109 (2014) 1302–1318], and it is able to detect certain type of departure from the null hypothesis of conditional mean independence without making any specific model assumptions.…

高维线性模型的同时推断AI 解读

This article proposes a bootstrap-assisted procedure to conduct simultaneous inference for high-dimensional sparse linear models based on the recent desparsifying Lasso estimator. Our procedure allows the dimension of the parameter vector of interest to be exponentially larger than sample size, and it automatically accounts for the dependence within the desparsifying Lasso estimator. Moreover, our simultaneous testing method can be naturally coupled with the margin screening…

函数型时间序列的白噪声检验与模型诊断AI 解读

This paper is concerned with white noise testing and model diagnostic checking for stationary functional time series. To test for the functional white noise null hypothesis, we propose a Cramér–von Mises type test based on the functional periodogram introduced by Panaretos and Tavakoli (2013a). Using the Hilbert space approach, we derive the asymptotic distribution of the test statistic under suitable assumptions. A new block bootstrap procedure is introduced to obtain the…

广义经验似然估计框架中的固定平滑渐近理论AI 解读

This paper concerns the fixed-smoothing asymptotics for two commonly used estimators in the generalized empirical likelihood estimation framework for time series data, namely the continuous updating estimator and the maximum blockwise empirical likelihood estimator. For continuously updating generalized method of moments (GMM) estimator, we show that the results for the two-step GMM estimator in Sun (2014a) continue to hold under suitable assumptions. For continuous updating…

时间序列经验似然方法的覆盖率上界问题AI 解读

Summary The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide…

时间序列的固定平滑渐近理论AI 解读

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based $t$-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order…

时间序列变点检验AI 解读

This article considers the CUSUM-based (cumulative sum) test for a change point in a time series. In the case of testing for a mean shift, the traditional Kolmogorov–Smirnov test statistic involves a consistent long-run variance estimator, which is needed to make the limiting null distribution free of nuisance parameters. The commonly used lag-window type long-run variance estimator requires to choose a bandwidth parameter and its selection is a difficult task in practice.…