Related papers: Tests for high dimensional data based on means, sp…
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…
We discuss a one-sample location test that can be used in the case of high-dimensional data. For high-dimensional data, the power of Hotelling's test decrises when the dimension is close to the sample size. To address this loss of power,…
Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…
Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
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…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…
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…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
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…
We study a rank based univariate two-sample distribution-free test. The test statistic is the difference between the average of between-group rank distances and the average of within-group rank distances. This test statistic is closely…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…
We study the high-dimensional two-sample location problem under elliptical symmetry with arbitrary dependence in the scatter matrix. Existing spatial-sign procedures are attractive for heavy-tailed data, but their null calibration is tied…
The family of rank estimators, including Han's maximum rank correlation (Han, 1987) as a notable example, has been widely exploited in studying regression problems. For these estimators, although the linear index is introduced for…