Nonparametric estimation of multivariate scale mixtures of uniform densities

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• 作者：Marios G. Pavlides^a ; ^{marios.pavlides@gmail.com} ; Jon A. Wellner^b ; ^{jaw@stat.washington.edu}
• 关键词：62G05 ; 62G07 ; 62G20 ; 62F20 ; 62H12
• 刊名：Journal of Multivariate Analysis
• 出版年：2012
• 期刊代码：77_0047259x
• 类别：mt
• 出版时间：May, 2012
• 卷：107
• 期：Complete
• 页码：71-89
• 文件大小：442 K

摘要

Suppose that has a Uniform distribution, that has the distribution on , and let . The resulting class of distributions of (as varies over all distributions on ) is called the Scale Mixture of Uniforms class of distributions, and the corresponding class of densities on is denoted by . We study maximum likelihood estimation in the family . We prove existence of the MLE, establish Fenchel characterizations, and prove strong consistency of the almost surely unique maximum likelihood estimator (MLE) in . We also provide an asymptotic minimax lower bound for estimating the functional under reasonable differentiability assumptions on in a neighborhood of . We conclude the paper with discussion, conjectures and open problems pertaining to global and local rates of convergence of the MLE.