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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…

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 article, we address the challenge of identifying skilled mutual funds among a large pool of candidates, utilizing the linear factor pricing model. Assuming observable factors with a weak correlation structure for the idiosyncratic…

Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…

The Wilcoxon signed-rank test and the Wilcoxon-Mann-Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic…

We consider a testing problem for cross-sectional dependence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional dependence is described…

The sign and the signed-rank tests for univariate data are perhaps the most popular nonparametric competitors of the t test for paired sample problems. These tests have been extended in various ways for multivariate data in finite…

This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically…

In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by…

This article concerns tests for the two-sample location problem when the dimension is larger than the sample size. The traditional multivariate-rank-based procedures cannot be used in high dimensional settings because the sample scatter…

Testing for multi-dimensional white noise is an important subject in statistical inference. Such test in the high-dimensional case becomes an open problem waiting to be solved, especially when the dimension of a time series is comparable to…

We consider the problem of testing mutual independence among the components of a high-dimensional random vector. Building on the rank-based max-sum framework, we introduce fixed finite-$L_q$ power-sum statistics under three general classes…

Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously…

This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…

This paper investigates the robust linear discriminant analysis (LDA) problem with elliptical distributions in high-dimensional data. We propose a robust classification method, named SSLDA, that is intended to withstand heavy-tailed…

We introduce a new type of test for complete spatial randomness that applies to mapped point patterns in a rectangle or a cube of any dimension. This is the first test of its kind to be based on characteristic functions and utilizes a…

We propose a methodology to construct tests for the null hypothesis that the pricing errors of a panel of asset returns are jointly equal to zero in a linear factor asset pricing model -- that is, the null of "zero alpha". We consider, as a…

Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…

In this study, we focus on applying L-statistics to the high-dimensional one-sample location test problem. Intuitively, an L-statistic with $k$ parameters tends to perform optimally when the sparsity level of the alternative hypothesis…

In this paper, we study change-point testing for high-dimensional linear models, an important problem that has not been well explored in the literature. Specifically, we propose a quadratic-form cumulative sum (CUSUM) statistic to test the…