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On nonparametric maximum likelihood for a class of stochastic inverse problems

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  • ChafaI¨, Djalil
  • Loubes, Jean-Michel

Abstract

We establish the consistency of a nonparametric maximum likelihood estimator for a class of stochastic inverse problems. We proceed by embedding the framework into the general settings of early results of Pfanzagl related to mixtures [Pfanzagl, J., 1998a. Consistency of maximum likelihood estimators for certain nonparametric families, in particular: mixtures. J. Statist. Plann. Inference 19(2), 137-158, MR 89g:62063; Pfanzagl, J., 1998b. Large deviation inequality for maximum likelihood estimators for certain nonparametric families, in particular: mixtures. Ann. Stats. 19(2), 137-158, MR 89g:62063].

Suggested Citation

  • ChafaI¨, Djalil & Loubes, Jean-Michel, 2006. "On nonparametric maximum likelihood for a class of stochastic inverse problems," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1225-1237, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1225-1237
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    References listed on IDEAS

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    1. Priebe, Carey E. & Marchette, David J., 2000. "Alternating kernel and mixture density estimates," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 43-65, November.
    2. Tze Leung Lai, 2003. "Nonparametric estimation in nonlinear mixed effects models," Biometrika, Biometrika Trust, vol. 90(1), pages 1-13, March.
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    Cited by:

    1. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    2. Antic, J. & Laffont, C.M. & Chafaï, D. & Concordet, D., 2009. "Comparison of nonparametric methods in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 642-656, January.

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