MOMENT-MATCHING AND BEST ENTROPY ESTIMATION

[摘要] Given the first n moments of an unknown function xBAR on the unit interval, a common estimate of xBAR is psi(pi(n)), where pi(n) is a polynomial of degree n taking values in a prescribed interval, psi is a given monotone function, and pi(n) is chosen so that the moments of psi(pi(n)) equal those of xBAR. This moment-matching procedure is closely related to best entropy estimation of xBAR: two classical cases arise when psi is the exponential function (corresponding to the Boltzmann-Shannon entropy) and the reciprocal function (corresponding to the Burg entropy). General conditions ensuring the existence and uniqueness of pi(n) are given using convex programming duality techniques, and it is shown that the estimate psi(pi(n)) converges uniformly to xBAR providing xBAR is sufficiently smooth. (C) 1994 Academic Press, Inc.

[发布日期] 1994-08-01