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Representations for eigenfunctions of expected value operators in the Wishart distribution

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  • Richards, Donald

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)) = [lambda]nf([Sigma]) for some [lambda]n [epsilon] , whenever the m x m matrix S has the Wishart distribution W(m, n, [Sigma]). 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.

Suggested Citation

  • Richards, Donald, 1983. "Representations for eigenfunctions of expected value operators in the Wishart distribution," Statistics & Probability Letters, Elsevier, vol. 1(3), pages 141-145, March.
    • Handle: RePEc:eee:stapro:v:1:y:1983:i:3:p:141-145
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