Multivariate sign-based high-dimensional tests for sphericity
成果类型：
Article
署名作者：
Zou, Changliang; Peng, Liuhua; Feng, Long; Wang, Zhaojun
署名单位：
Nankai University
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/ast040
发表日期：
2014
页码：
229236
关键词：
摘要：
This article concerns tests for sphericity in cases where the data dimension is larger than the sample size. The existing multivariate sign-based procedure (Hallin & Paindaveine, 2006) for sphericity is not robust with respect to high dimensionality, producing tests with Type I error rates that are much larger than the nominal levels. This is mainly due to bias from estimating the location parameter. We develop a correction that makes the existing test statistic robust with respect to high dimensionality, and show that the proposed test statistic is asymptotically normal under elliptical distributions. The proposed method allows the dimensionality to increase as the square of the sample size. Simulations demonstrate that it has good size and power in a wide range of settings.