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Sieved Maximum Likelihood Estimation in Wicksell's Problem and Related Deconvolution Problems
Author(s) -
Jongbloed Geurt
Publication year - 2001
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00230
Subject(s) - mathematics , deconvolution , estimator , convolution (computer science) , minimax estimator , kernel (algebra) , blind deconvolution , minimum variance unbiased estimator , mathematical optimization , statistics , combinatorics , artificial intelligence , artificial neural network , computer science
It is shown that the classical Wicksell problem is related to a deconvolution problem where the convolution kernel is unbounded, convex and decreasing on (0, ∞). For that type of deconvolution problems, the usual non‐parametric maximum likelihood estimator of the distribution function is shown not to exist. A sieved maximum likelihood estimator is defined, and some algorithms are described that can be used to compute this estimator. Moreover, this estimator is proved to be strongly consistent.