Characterization of conditional covariance and unified theory in the problem of ordering random variables |
| |
Authors: | Kentaro Nomakuchi Toshio Sakata |
| |
Institution: | (1) Department of mathematics, Faculty of Science, Kyushu University, Higashi-ku, 812 Fukuoka, Japan;(2) Faculty of General Education, Kumamoto University, 860 Kumamoto, Japan |
| |
Abstract: | Under the assumption that a (p+q)-dimensional row vector (Y, X) is elliptically contoured distributed, the conditional covariance of Y given X=x is characterized in the context of correctly ordering the coordinates Y
k
's of Y based on X. This is an answer to a conjecture implicit in Portnoy (1982). Moreover some unified theory is presented for the problem of ordering Y
k
's based on X. An essential tool is the decreasing in transposition (D. T.) function theory of Hollander et al. (1977, Ann. Statist., 5(4), 722–733). |
| |
Keywords: | Linear predictor ordering r v 's elliptically contoured distribution |
本文献已被 SpringerLink 等数据库收录! |
|