Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces

TrungTin Nguyen, Faicel Chamroukhi, Hien D. Nguyen and Geoffrey J. McLachlan

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 14, 5048-5059

Abstract: The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We establish and prove the following results: to an arbitrary degree of accuracy, (a) location-scale mixtures of a continuous probability density function (PDF) can approximate any continuous PDF, uniformly, on a compact set; and (b) for any finite p≥1, location-scale mixtures of an essentially bounded PDF can approximate any PDF in Lp, in the Lp norm.

Date: 2023
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DOI: 10.1080/03610926.2021.2002360

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