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 -