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On approximations via convolution-defined mixture models

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  • Hien D. Nguyen
  • Geoffrey McLachlan

Abstract

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.

Suggested Citation

  • Hien D. Nguyen & Geoffrey McLachlan, 2019. "On approximations via convolution-defined mixture models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(16), pages 3945-3955, August.
  • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:16:p:3945-3955
    DOI: 10.1080/03610926.2018.1487069
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    Cited by:

    1. Muhammed Taher Al-Mudafer & Benjamin Avanzi & Greg Taylor & Bernard Wong, 2021. "Stochastic loss reserving with mixture density neural networks," Papers 2108.07924, arXiv.org.
    2. Daan de Waal & Tristan Harris & Alta de Waal & Jocelyn Mazarura, 2022. "Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution," Mathematics, MDPI, vol. 10(14), pages 1-20, July.

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