Nonparametric maximum likelihood estimation for the multisample Wicksell corpuscle problem

• 成果类型: Article
• 署名作者: Chan, Kwun Chuen Gary; Qin, Jing
• 署名单位: University of Washington; University of Washington Seattle; National Institutes of Health (NIH) - USA; NIH National Institute of Allergy & Infectious Diseases (NIAID)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw011
• 发表日期: 2016
• 页码: 273286
• 关键词: sphere size distributions; selection bias models; empirical distributions; emission-tomography; particle-size; stereology

摘要

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.