Representations for eigenfunctions of expected value operators in the Wishart distribution

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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)) = 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.

Original languageEnglish (US)
Pages (from-to)141-145
Number of pages5
JournalStatistics and Probability Letters
Volume1
Issue number3
DOIs
Publication statusPublished - Mar 1983

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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