Characterization of distributions symmetric with respect to a group of transformations and testing of corresponding statistical hypothesis

L. B. Klebanov, T. J. Kozubowski, S. T. Rachev and V. E. Volkovich

Statistics & Probability Letters, 2001, vol. 53, issue 3, 241-247

Abstract: It is shown that for a real orthogonal matrix A, a real number r[set membership, variant](0,2), and two i.i.d. random vectors X and Y, the inequality is valid, with equality if and only if the distribution of X is invariant with respect to the group generated by the matrix A. Some generalizations of this property are also given and a statistical test for the corresponding hypothesis is proposed.

Keywords: Empirical; characteristic; function; Moment; properties; Negative-definite; kernel; Probability; metric; Stochastic; inequality (search for similar items in EconPapers)
Date: 2001
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