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Nonparametric maximum likelihood estimation in a non locally compact setting

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Abstract

Maximum likelihood estimation is considered in the context of infinite dimensional parameter spaces. It is shown that in some locally convex parameter spaces sequential compactness of the bounded sets ensures the existence of minimizers of objective functions and the consistency of maximum likelihood estimators in an appropriate topology. The theory is applied to revisit some classical problems of nonparametric maximum likelihood estimation, to study location parameters in Banach spaces, and finally to obtain Varadarajan’s theorem on the convergence of empirical measures in the form of a consistency result for a sequence of maximum likelihood estimators. Several parameter spaces sharing the crucial compactness property are identified.

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Authors and Affiliations

  1. Département de Mathématiques et de Statistique, Université Laval, G1K 7P4, Québec, Canada

    Jean-Claude Massé

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  1. Jean-Claude Massé
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Additional information

This research was supported by grants from the National Sciences and Engineering Research Council of Canada and the Fonds FCAR de la Province de Québec.

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Massé, JC. Nonparametric maximum likelihood estimation in a non locally compact setting. Metrika 46, 123–145 (1997). https://doi.org/10.1007/BF02717170

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  • DOI: https://doi.org/10.1007/BF02717170

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