Related papers: Adaptive Sphericity Tests for High Dimensional Dat…
We consider testing zero pricing errors in high-dimensional linear factor pricing models. Existing methods are mainly based on either an $L_2$ statistic, which is effective under dense alternatives, or an $L_\infty$ statistic, which is…
We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…
We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance…
In this paper, we propose corrections to the likelihood ratio test and John's test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…
This paper investigates change point inference in high-dimensional time series. We begin by introducing a max-$L_2$-norm based test procedure, which demonstrates strong performance under dense alternatives. We then establish the asymptotic…
Testing large covariance matrices is of fundamental importance in statistical analysis with high-dimensional data. In the past decade, three types of test statistics have been studied in the literature: quadratic form statistics, maximum…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
We consider an analysis of variance type problem, where the sample observations are random elements in an infinite dimensional space. This scenario covers the case, where the observations are random functions. For such a problem, we propose…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic…
High-dimensional changepoint inference, adaptable to diverse alternative scenarios, has attracted significant attention in recent years. In this paper, we propose an adaptive and robust approach to changepoint testing. Specifically, by…
This paper develops a novel methodology for testing the goodness-of-fit of sparse parametric regression models based on projected empirical processes and p-value combination, where the covariate dimension may substantially exceed the sample…
In the context of high-dimensional data, we investigate the one-sample location testing problem. We introduce a max-type test based on the weighted spatial sign, which exhibits exceptional performance, particularly in the presence of sparse…
Sphericity test plays a key role in many statistical problems. We propose Spearman's rho-type rank test and Kendall's tau-type rank test for sphericity in the high dimensional settings. We show that these two tests are equivalent. Thanks to…
Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for…
In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…
Diversity maximization is an important concept in information retrieval, computational geometry and operations research. Usually, it is a variant of the following problem: Given a ground set, constraints, and a function $f(\cdot)$ that…
We propose a two-sample test for covariance matrices in the high-dimensional regime, where the dimension diverges proportionally to the sample size. Our hybrid test combines a Frobenius-norm-based statistic as considered in Li and Chen…
In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel…