On nonparametric maximum likelihood for a class of stochastic inverse problems

2004/11/23 by Djalil Chafaï, Djalil Chafai, Jean–Michel Loubes +1 · 1 citation
Mathematics · #Applied mathematics #Artificial intelligence #Class (philosophy) #Econometrics #Inverse #Mathematics #Maximum likelihood #Nonparametric statistics #Numerical methods in inverse problems #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics #math.ST #msc:34K29 #msc:62G05 #stat.TH

paper · pdf · doi:10.1016/j.spl.2005.12.019

published as Statistics & Probability Letters / Statistics and Probability Letters 76, 12 (2006) 1225-1237

arxiv created 2004/11/23 · openalex publication_date 2006/01/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Convergence of a stochastic approximation version of the EM algorithm
• Large-Sample Inference for Log-Spline Models
• The Geometry of Mixture Likelihoods: A General Theory
• Sobolev Spaces

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• On the strong consistency of asymptotic -estimators