Nonparametric maximum likelihood estimation for the multisample Wicksell corpuscle problem.
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.
Department of Biostatistics, University of Washington, Seattle, Washington 98195, U.S.A.
Kwun Chuen Gary
KC
Chan
Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, Maryland 20892, U.S.A. , jingqin@niaid.nih.gov.
Jing
J
Qin
Abel-type integral equation; Expectation-maximization algorithm; Indirect measurement; Particle size