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arXiv · 2008.09787

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

TrungTin Nguyen·Faicel Chamroukhi·Hien D Nguyen·Geoffrey J McLachlan
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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 $p\ge1$, location-scale mixtures of an essentially bounded PDF can approximate any PDF in $\mathcal{L}_{p}$, in the $\mathcal{L}_{p}$ norm.

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TrungTin Nguyen, Faicel Chamroukhi, Hien D Nguyen, Geoffrey J McLachlan. 2020-08-22. Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces. https://arxiv.org/abs/2008.09787

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