TY - JOUR

T1 - Characterization of distributions symmetric with respect to a group of transformations and testing of corresponding statistical hypothesis

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

UR - http://www.scopus.com/inward/record.url?scp=0041401416&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0041401416

VL - 53

SP - 241

EP - 247

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 3

ER -