Constant Regression Polynomials and the Wishart Distribution
Copyright policy )Constant Regression Polynomials and the Wishart Distribution
Summary: Results are obtained for the problems of constructing and characterizing scalar-valued polynomial statistics having constant regression on the mean of a random sample of Wishart matrices. The construction procedure introduced by \textit{B. Heller} [J. Multivariate Anal. 14, 101-104 (1984; Zbl 0541.62034)] is generalized to show that certain polynomials in the principal minors of the sample matrices have zero regression on the mean. The zero-regression polynomials are characterized through expectations involving certain matrix-valued Bessel functions of \textit{K. I. Gross} and \textit{R. A. Kunze} [J. Funct. Anal. 22, 73-105 (1976; Zbl 0322.43014)]. It is shown that the zero-regression property characterizes Wishart distributions within a wide family of mixtures of Wishart distributions.
- University of Virginia United States
scalar-valued polynomial statistics, Wishart matrices, Analysis on other specific Lie groups, zero- regression polynomials, constant regression, mixtures of Wishart distributions, matrix-valued Bessel functions, Multivariate distribution of statistics, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Characterization and structure theory for multivariate probability distributions; copulas, hyperbolic differential operator, unitary representation
scalar-valued polynomial statistics, Wishart matrices, Analysis on other specific Lie groups, zero- regression polynomials, constant regression, mixtures of Wishart distributions, matrix-valued Bessel functions, Multivariate distribution of statistics, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Characterization and structure theory for multivariate probability distributions; copulas, hyperbolic differential operator, unitary representation
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