Representations for eigenfunctions of expected value operators in the Wishart distribution

Donald Richards

doi:10.1016/0167-7152(83)90062-7

Representations for eigenfunctions of expected value operators in the Wishart distribution

Donald Richards

Statistics

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Abstract

Recent articles by Kushner and Meisner (1980) and Kushner, Lebow and Meisner (1981) have posed the problem of characterising the 'EP' functions f(S) for which Ef(S) for which E(f(S)) = λ_nf(Σ) for some λ_n ε{lunate} R, whenever the m × m matrix S has the Wishart distribution W(m, n, Σ). In this article we obtain integral representations for all nonnegative EP functions. It is also shown that any bounded EP function is harmonic, and that EP polynomials may be used to approximate the functions in certain L^p spaces.

Original language	English (US)
Pages (from-to)	141-145
Number of pages	5
Journal	Statistics and Probability Letters
Volume	1
Issue number	3
DOIs	https://doi.org/10.1016/0167-7152(83)90062-7
State	Published - Mar 1983

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/0167-7152(83)90062-7

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AB - Recent articles by Kushner and Meisner (1980) and Kushner, Lebow and Meisner (1981) have posed the problem of characterising the 'EP' functions f(S) for which Ef(S) for which E(f(S)) = λnf(Σ) for some λn ε{lunate} R, whenever the m × m matrix S has the Wishart distribution W(m, n, Σ). In this article we obtain integral representations for all nonnegative EP functions. It is also shown that any bounded EP function is harmonic, and that EP polynomials may be used to approximate the functions in certain Lp spaces.

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Representations for eigenfunctions of expected value operators in the Wishart distribution

Abstract

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