Canadian Journal of Statistics

Consistency of maximum likelihood estimators in a large class of deconvolution models

Journal Article

Abstract

We consider the maximum likelihood estimator equation image 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 equation image is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for equation image are derived, including uniform strong consistency. The Canadian Journal of Statistics 41: 98–110; 2013 © 2012 Statistical Society of Canada

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