Nonparametric maximum likelihood estimation for the multisample Wicksell corpuscle problem

Kwun Chuen Gary Chan and Jing Qin

Biometrika, 2016, vol. 103, issue 2, 273-286

Abstract: We study nonparametric maximum likelihood estimation for the distribution of spherical radii using samples containing a mixture of one-dimensional, two-dimensional biased and three-dimensional unbiased observations. Since direct maximization of the likelihood function is intractable, we propose an expectation-maximization algorithm for implementing the estimator, which handles an indirect measurement problem and a sampling bias problem separately in the E- and M-steps, and circumvents the need to solve an Abel-type integral equation, which creates numerical instability in the one-sample problem. Extensions to ellipsoids are studied and connections to multiplicative censoring are discussed.

Date: 2016
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