Nonparametric maximum likelihood estimation for the multisample Wicksell corpuscle problem
研究了利用一维、二维有偏和三维无偏观测的混合样本，对球体半径分布进行非参数最大似然估计，并提出了EM算法来避免直接求解不稳定的Abel型积分方程。
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.