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, V. E. Volkovich

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

It is shown that for a real orthogonal matrix A, a real number r∈(0,2), and two i.i.d. random vectors X and Y, the inequality E||X-AY||r≥E||X-Y||r 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.

Original languageEnglish
Pages (from-to)241-247
Number of pages7
JournalStatistics and Probability Letters
Volume53
Issue number3
DOIs
StatePublished - Jun 15 2001

Keywords

  • Empirical characteristic function
  • Moment properties
  • Negative-definite kernel
  • Probability metric
  • Stochastic inequality

Fingerprint Dive into the research topics of 'Characterization of distributions symmetric with respect to a group of transformations and testing of corresponding statistical hypothesis'. Together they form a unique fingerprint.

Cite this