Consistency of maximum likelihood estimators in a large class of deconvolution models |
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Authors: | Piet Groeneboom Geurt Jongbloed Stefanie Michael |
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Institution: | 1. Technische Universiteit Delft, Delft, The Netherlands;2. Talanx AG, Riethorst 2, 30659 Hannover, Germany |
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Abstract: | We consider the maximum likelihood estimator $\hat{F}_n$ of a distribution function in a class of deconvolution models where the known density of the noise variable is of bounded variation. This class of noise densities contains in particular bounded, decreasing densities. The estimator $\hat{F}_n$ is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for $\hat{F}_n$ are derived, including uniform strong consistency. The Canadian Journal of Statistics 41: 98–110; 2013 © 2012 Statistical Society of Canada |
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Keywords: | Empirical process theory inverse problem nonparametric estimation MSC 2010: Primary 62G05 secondary 62G20 |
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