Sieved Maximum Likelihood Estimation in Wicksell's Problem and Related Deconvolution Problems

Geurt Jongbloed

Scandinavian Journal of Statistics, 2001, vol. 28, issue 1, 161-183

Abstract: 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.

Date: 2001
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