Related papers: High-dimensional tests for spherical location and …

This paper considers testing a covariance matrix $\Sigma$ in the high dimensional setting where the dimension $p$ can be comparable or much larger than the sample size $n$. The problem of testing the hypothesis $H_0:\Sigma=\Sigma_0$ for a…

We derive the limit null distribution of the class of Sobolev tests of uniformity on the hypersphere when the dimension and the sample size diverge to infinity at arbitrary rates. The limiting non-null behavior of these tests is obtained…

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…

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This…

Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…

We revisit the null distribution of the high-dimensional spatial-sign test of Wang et al. (2015) under mild structural assumptions on the scatter matrix. We show that the standardized test statistic converges to a non-Gaussian limit,…

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…

We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider…

We consider the change point testing problem for high-dimensional time series. Unlike conventional approaches, where one tests whether the difference $\delta$ of the mean vectors before and after the change point is equal to zero, we argue…

In this paper, we are concerned with the independence test for $k$ high-dimensional sub-vectors of a normal vector, with fixed positive integer $k$. A natural high-dimensional extension of the classical sample correlation matrix, namely…

This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow much faster than the sample size with $ p…

We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…

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…

While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…

This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…

Change-point detection has been a classical problem in statistics and econometrics. This work focuses on the problem of detecting abrupt distributional changes in the data-generating distribution of a sequence of high-dimensional…

We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…

For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…