Testing for affine equivalence of elliptically symmetric distributions

Authors:
A. K. Gupta;N. Henze;B. Klar
Affiliations:
Department of Mathematics & Statistics, Bowling Green State University, OH;Institute of Mathematical Stochastics, University of Karlsruhe, Englerstr. 2, Karlsruhe 76128, Germany;Institute of Mathematical Stochastics, University of Karlsruhe, Englerstr. 2, Karlsruhe 76128, Germany
Venue:
Journal of Multivariate Analysis
Year:
2004

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Abstract

Let X and Y be d-dimensional random vectors having elliptically symmetric distributions. Call X and Y affinely equivalent if Y has the same distribution as AX + b for some nonsingular d × d-matrix A and some b ∈ Rd. This paper studies a class of affine invariant tests for affine equivalence under certain moment restrictions. The test statistics are measures of discrepancy between the empirical distributions of the norm of suitably standardized data.