Related papers: High-Dimensional Two-Sample Test for Elliptical Sy…
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,…
This article concerns tests for the two-sample location problem when the dimension is larger than the sample size. The traditional multivariate-rank-based procedures cannot be used in high dimensional settings because the sample scatter…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
In this paper, we consider the problem of testing the mean vector in the high dimensional settings. We proposed a new robust scalar transform invariant test based on spatial sign. The proposed test statistic is asymptotically normal under…
We develop some graph-based tests for spherical symmetry of a multivariate distribution using a method based on data augmentation. These tests are constructed using a new notion of signs and ranks that are computed along a path obtained by…
The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
We develop high-dimensional goodness-of-fit tests for elliptical models by testing radial--directional independence after affine standardization. The method forms coordinatewise correlations between the log-radius and directional…
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 construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector $X$ with finite mean has a spherical distribution if and only if $\Ex[u^\top X | v^\top X] = 0$ holds for any two…
We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…
This paper is concerned with testing global null hypotheses about population mean vectors of high-dimensional data. Current tests require either strong mixing (independence) conditions on the individual components of the high-dimensional…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…
Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully…
We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…
In this paper, for the problem of heteroskedastic general linear hypothesis testing (GLHT) in high-dimensional settings, we propose a random integration method based on the reference L2-norm to deal with such problems. The asymptotic…
In this paper, we propose a new scalar and shift transform invariant test statistic for the high-dimensional two-sample location test. The expectation of our test is exactly zero under the null hypothesis. And we allow the dimension could…