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 |
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Pages (from-to) | 241-247 |
Number of pages | 7 |
Journal | Statistics and Probability Letters |
Volume | 53 |
Issue number | 3 |
DOIs | |
State | Published - Jun 15 2001 |
Keywords
- Empirical characteristic function
- Moment properties
- Negative-definite kernel
- Probability metric
- Stochastic inequality