Journal
BIOMETRIKA
Volume 101, Issue 1, Pages 229-236Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/ast040
Keywords
Asymptotic normality; Large p; small n; Spatial median; Spatial sign; Sphericity test
Funding
- National Natural Science Foundation
- Research Fund for the Doctoral Program of Higher Education of China
- Foundation for the Authors of National Excellent Doctoral Dissertations
- Program for New Century Excellent Talents in University
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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.
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