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

doi:10.1016/S0167-7152(01)00011-6

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

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	241-247
Number of pages	7
Journal	Statistics and Probability Letters
Volume	53
Issue number	3
DOIs	https://doi.org/10.1016/S0167-7152(01)00011-6
State	Published - Jun 15 2001

Keywords

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

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10.1016/S0167-7152(01)00011-6

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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.",

keywords = "Empirical characteristic function, Moment properties, Negative-definite kernel, Probability metric, Stochastic inequality",

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AU - Klebanov, L. B.

AU - Kozubowski, T. J.

AU - Rachev, S. T.

AU - Volkovich, V. E.

PY - 2001/6/15

Y1 - 2001/6/15

N2 - 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.

AB - 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.

KW - Empirical characteristic function

KW - Moment properties

KW - Negative-definite kernel

KW - Probability metric

KW - Stochastic inequality

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U2 - 10.1016/S0167-7152(01)00011-6

DO - 10.1016/S0167-7152(01)00011-6

M3 - Article

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VL - 53

SP - 241

EP - 247

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 3

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