Related papers: Testing for Independence of Large Dimensional Vect…

Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…

This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…

Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econometricians began to turn their attention to the problem in the presence of serial…

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…

We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic…

For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…

Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

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…

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…

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…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…

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…

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…

We introduce two novel non-parametric statistical hypothesis tests. The first test, called the relative test of dependency, enables us to determine whether one source variable is significantly more dependent on a first target variable or a…

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…

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…

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…