Related papers: Deviation Tests for a High-dimensional Mean
Statistical inference for high-dimensional regression heteroskedasticity is an important but under-explored problem. The current paper aims at filling this gap by proposing two tests, namely the variance difference test and the variance…
Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…
Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…
The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…
Detecting a minor average treatment effect is a major challenge in large-scale applications, where even minimal improvements can have a significant economic impact. Traditional methods, reliant on normal distribution-based or expanded…
This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…
This paper deals with studying vague convergence of random measures of the form $\mu_{n}=\sum_{i=1}^{n} p_{i,n} \delta_{\theta_i}$, where $(\theta_i)_{1\le i \le n}$ is a sequence of independent and identically distributed random variables…
Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this…
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…
In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…