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Parameter recovery in two-component contamination mixtures: the L2 strategy

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  • Gadat, Sébastien
  • Marteau, Clément
  • Maugis, Cathy

Abstract

In this paper, we consider a parametric density contamination model. We work with a sample of i.i.d. data with a common density, f* = (1 - lambda*)phi + lambda*phi (. - mu*), where the shape phi is assumed to be known. We establish the optimal rates of convergence for the estimation of the mixture parameters (lambda*, mu*) is an element of (0, 1) x R-d. In particular, we prove that the classical parametric rate 1/ root n cannot be reached when at least one of these parameters is allowed to tend to 0 with n.
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Suggested Citation

  • 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.
    • Handle: RePEc:tse:wpaper:30481
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    1. 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.
    2. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.
    3. 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. 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.

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