Indeterminate Hamburger moment problem: Entropy convergence

Pier Luigi Novi Inverardi, Aldo Tagliani and Mariyan Milev

Statistics & Probability Letters, 2024, vol. 212, issue C

Abstract: The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it fhmax. It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to fhmax where the value of its entropy can be finite or −∞.

Keywords: Moments; Hamburger moment problem; Hankel matrix; Maximum entropy; Entropy convergence (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2024.110155

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