Related papers: High dimensional Mean Test for Temporal Dependent …
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…
We study the following fundamental hypothesis testing problem, which we term Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on $\mathbb{R}^d$, the task is to distinguish, with high probability, between the following…
This paper investigates the problem of detecting relevant change points in the mean vector, say $\mu_t =(\mu_{1,t},\ldots ,\mu_{d,t})^T$ of a high dimensional time series $(Z_t)_{t\in \mathbb{Z}}$. While the recent literature on testing for…
In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by the recent U-statistic based retrospective tests developed by Wang et al.(2019) and Zhang et al.(2020),…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…
We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
While powerful methods have been developed for high-dimensional hypothesis testing assuming orthogonal parameters, current approaches struggle to generalize to the more common non-orthogonal case. We propose Stable Distillation (SD), a…
Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
In this paper, we discuss tests for mean vector of high-dimensional data when the dimension $p$ is a function of sample size $n$. One of the tests, called the decomposite $T^{2}$-test, in the high-dimensional testing problem is constructed…
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
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…
A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…