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Semiparametric Mixtures of Symmetric Distributions

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  • Cristina Butucea
  • Pierre Vandekerkhove

Abstract

type="main" xml:id="sjos12015-abs-0001"> We consider in this paper the semiparametric mixture of two unknown distributions equal up to a location parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. To insure the identifiability of the model, it is assumed that the mixed distribution is zero symmetric, the model being then defined by the mixing proportion, two location parameters and the probability density function of the mixed distribution. We propose a new class of M-estimators of these parameters based on a Fourier approach and prove that they are n -consistent under mild regularity conditions. Their finite sample properties are illustrated by a Monte Carlo study, and a benchmark real dataset is also studied with our method.

Suggested Citation

  • Cristina Butucea & Pierre Vandekerkhove, 2014. "Semiparametric Mixtures of Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 227-239, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:227-239
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    File URL: http://hdl.handle.net/10.1111/sjos.12015
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    References listed on IDEAS

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    1. Lancaster, Tony & Imbens, Guido, 1996. "Case-control studies with contaminated controls," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 145-160.
    2. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
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    1. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    2. De Castro, Y. & Gadat, Sébastien & Marteau, Clément & Maugis, Cathy, 2019. "SuperMix: Sparse Regularization for Mixture," TSE Working Papers 19-1040, Toulouse School of Economics (TSE), revised Sep 2020.
    3. Yuichi Kitamura & Louise Laage, 2018. "Nonparametric Analysis of Finite Mixtures," Papers 1811.02727, arXiv.org.
    4. Hu, Hao & Wu, Yichao & Yao, Weixin, 2016. "Maximum likelihood estimation of the mixture of log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 137-147.
    5. Gadat, Sébastien & Marteau, Clément & Maugis, Cathy, 2016. "Parameter recovery in two-component contamination mixtures: the L2 strategy," TSE Working Papers 16-653, Toulouse School of Economics (TSE), revised Feb 2018.
    6. Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 65-87, March.

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