TY - JOUR
T1 - Representations for eigenfunctions of expected value operators in the Wishart distribution
AU - Richards, Donald
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1983/3
Y1 - 1983/3
N2 - 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.
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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U2 - 10.1016/0167-7152(83)90062-7
DO - 10.1016/0167-7152(83)90062-7
M3 - Article
AN - SCOPUS:0000081399
SN - 0167-7152
VL - 1
SP - 141
EP - 145
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 3
ER -