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

2020/08/22 by TrungTin Nguyen, Faïcel Chamroukhi, Nguyen, TrungTin +5 · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Inference #Statistical Methods and Bayesian Inference

paper · doi:10.48550/arxiv.2008.09787

Abstract

The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We 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 L_p, in the L_p norm.

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