title: A High-Dimensional Nonparametric Multivariate Test for Mean Vector.
abstract: This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector, based on modifying the classical HotellingT2test, have been proposed in the literature. Despite their usefulness, they tend to have unsatisfactory power performance for heavy-tailed multivariate data, which frequently arise in genomics and quantitative finance. This paper proposes a novel high-dimensional nonparametric test for the population mean vector for a general class of multivariate distributions. With the aid of new tools in modern probability theory, we proved that the limiting null distribution of the proposed test is normal under mild conditions whenpis substantially larger thann. We further study the local power of the proposed test and compare its relative efficiency with a modified HotellingT2test for high-dimensional data. An interesting finding is that the newly proposed test can have even more substantial power gain with largepthan the traditional nonparametric multivariate test does with finite fixedp. We study the finite sample performance of the proposed test via Monte Carlo simulations. We further illustrate its application by an empirical analysis of a genomics data set.
authors: Associate Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455.
authors: Lan
authors: L
authors: Wang
authors: Graduate student, School of Statistics, University of Minnesota, Minneapolis, MN 55455.
authors: Bo
authors: B
authors: Peng
authors: Distinguished Professor, Department of Statistics and the Methodology Center, the Pennsylvania State University, University Park, PA 16802-2111.
authors: Runze
authors: R
authors: Li
keywords: Asymptotic relative efficiency; High dimensional multivariate data; Hotelling T2 test; Nonparametric multivariate test