Consistency of maximum likelihood estimators in a large class of deconvolution models. Issue 1 (7th September 2012)

• Record Type: Journal Article
• Authors: Groeneboom, Piet; Jongbloed, Geurt; Michael, Stefanie
• Is Part Of: Canadian journal of statistics. Volume 41:Issue 1(2013)
• Page Start: 98
• Page End: 110
• Publication Date: 2012-09-07
• Subjects: Mathematical statistics -- Periodicals; 519.5
• DOI: 10.1002/cjs.11152
• Languages: English
• ISSNs: 0319-5724

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We consider the maximum likelihood estimator <tex-math notation="tex"><![CDATA[$\hat{F}_n$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg36s6rv02" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> 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 <tex-math notation="tex"><![CDATA[$\hat{F}_n$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg36s6rtts" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for <tex-math notation="tex"><![CDATA[$\hat{F}_n$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg36s6rtww" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> are derived, including uniform strong consistency. <italic>The Canadian Journal of Statistics</italic> 41: 98–110; 2013 © 2012 Statistical Society of Canada</p> </abstract>