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Convergence of best entropy estimates

Borwein, Jonathan M. and Lewis, Adrian (1991) Convergence of best entropy estimates. SIAM J. Optimization, 1 . pp. 191-205.

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    Abstract

    Given a finite number of moments of an unknown density ̅ x on a finite measure space, the best entropy estimate-that nonnegative density x with the given moments which minimizes the Boltzmann-Shannon entropy I(x):=∫ x log x-is considered. A direct proof is given that I has the Kadec property in L1-if Yn converges weakly to ̅y and I(yn) converges to I( ̅y ), then ynn converges to ̅y in norm. As a corollary, it is obtained that, as the number of given moments increases, the best entropy estimates converge in L1 norm to the best entropy estimate of the limiting problem, which is simply ̅ x in the determined case. Furthermore, for classical moment problems on intervals with ̅ x strictly positive and sufficiently smooth, error bounds and uniform convergence are actually obtained.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 18 Feb 2015 14:51
    Last Modified: 18 Feb 2015 14:51
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1576

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