Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 3, 653--677

RANK-BASED PROCEDURES FOR STRUCTURAL HYPOTHESES ON COVARIANCE MATRICES

By

JOHN MARDEN, University of Illinois, Urbana-Champaign, USA
and
YONGHONG GAO, University of Missouri, Kansas City, USA

SUMMARY. Multivariate sign- and rank-based procedures are developed for structural hypotheses on covariance matrices defined through group symmetries. We show these test statistics are asymptotically chi-square distributed, and calculate their asymptotic relative efficiencies with respect to conventional parametric test statistics. The efficiency calculations and a simulation study suggest that the rank procedures are competitive with the usual normal-theory procedures under normality, and can be quite a bit better under heavy-tailed distributions. The sign procedures are somewhat less efficient, but better at very heavy tails.

AMS (1991) subject classification}. Primary 62H15, 62F35; secondary 62F03.

Key words and phrases. Multivariate signs, multivariate ranks, structural hypotheses, covariance matrices, intraclass correlation.

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