Nonparametric Tests for Multivariate Association

Symmetry

Solomon W. Harrar¹  Yan Xu² 

[1] Dr. Bing Zhang Department of Statistics, College of Arts and Sciences, University of Kentucky, Lexington, KY 40506, USA;Merck & Co., 351 North Sumneytown Pike, P.O. Box 1000, North Wales, PA 19454, USA;

关键词: multivariate data;    nonparametric;    MANOVA;    lack-of-fit test;    large number of groups;   

DOI  :  10.3390/sym14061112

来源: DOAJ

【 摘 要 】

Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent results in MANOVA tests for a large number of groups. Two types of tests are proposed. While it is natural to consider the classical approach for constructing the test by jointly considering all the variables together, we also investigate a composite test where variable-by-variable univariate tests are combined to form a multivariate test. The asymptotic distributions of the test statistics are derived in a unified manner by deriving the asymptotic matrix variate normal distribution of random matrices involved in the construction of the statistics. The tests have good numerical performance in finite samples. The application of the methods is illustrated with gene expression profiling of bronchial airway brushings.

【 授权许可】

Unknown