A robust testing procedure for the equality of covariance matrices

In classical statistics the likelihood ratio statistic used in testing hypotheses about covariance matrices does not have a closed form distribution, but asymptotically under strong normality assumptions is a function of the χ 2 -distribution. This distributional approximation totally fails if the n...

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Bibliographic Details
Published in:Computational statistics & data analysis 2005-06, Vol.49 (3), p.863-874
Main Authors: Aslam, Shagufta, Rocke, David M.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Likelihood ratio test
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Parametric inference
Probability and statistics
S-estimate
Sciences and techniques of general use
Statistics
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Summary:In classical statistics the likelihood ratio statistic used in testing hypotheses about covariance matrices does not have a closed form distribution, but asymptotically under strong normality assumptions is a function of the χ 2 -distribution. This distributional approximation totally fails if the normality assumption is not completely met. In this paper we will present multivariate robust testing procedures for the scatter matrix Σ using S-estimates. We modify the classical likelihood ratio test (LRT) into a robust LRT by substituting the robust estimates in the formula in place of classical estimates. A nonlinear formula is also suggested to approximate the degrees of freedom for the approximated Wishart distribution proposed for S-estimates of the shape matrix Σ . We present simulation results to compare the validity and the efficiency of the robust likelihood test to the classical likelihood test.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2004.06.009