Nonparametric maximum likelihood estimation for the multisample Wicksell corpuscle problem

作者：Chan Kwun Chuen Gary^*; Qin Jing

来源：Biometrika, 2016, 103(2): 273-286.

DOI：10.1093/biomet/asw011

• Abel-type integral equation
• Expectation-maximization algorithm
• Indirect measurement
• Particle size

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.

• 出版日期2016-6