✦ LIBER ✦
Characterization of distributions symmetric with respect to a group of transformations and testing of corresponding statistical hypothesis
✍ Scribed by L.B. Klebanov; T.J. Kozubowski; S.T. Rachev; V.E. Volkovich
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 100 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
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.