The expected values of zonal polynomials of elliptically contoured distributions
The paper provides expressions for the expected values of zonal polynomials of matrix \(X'X\) in the case where X has a matrix elliptically contoured distribution. The work is based on results of similar nature provided by \textit{A. Constantine} [Ann. Math. Stat. 34, 1270-1285 (1963; Zbl 0123.368)], \textit{D. J. de Waal} [ibid. 43, 344-347 (1972; Zbl 0264.62017)], \textit{B. K. Shah} and \textit{C. G. Khatri} [Ann. Stat. 2, 833- 836 (1974; Zbl 0285.62026)], and \textit{R. J. Muirhead} [Aspects of multivariate statistical theory (New York, 1982)]. The examples that are provided include the multivariate t-distribution and the compound multivariate normal distribution. The fact that the expected values of the multivariate Cauchy distribution do not exist is an obvious consequence of the obtained results.
matrix elliptically contoured distribution
scientific article; zbMATH DE number 4199142
scientific article