A HYBRID ALGORITHM FOR COMPUTATION OF THE NONPARAMETRIC MAXIMUM-LIKELIHOOD ESTIMATOR FROM CENSORED-DATA

We present a hybrid algorithm for nonparametric maximum likelihood est imation from censored data when the log-likelihood is concave. The hyb rid algorithm uses a composite algorithmic mapping combining the expec tation-maximization (EM) algorithm and the (modified) iterative convex minorant (ICM) algorithm. Global convergence of the hybrid algorithm is proven; the iterates generated by the hybrid algorithm are shown to converge to the nonparametric maximum likelihood estimator (NPMLE) un ambiguously. Numerical simulations demonstrate that the hybrid algorit hm converges more rapidly than either of the EM or the naive ICM algor ithm for doubly censored data. The speed of the hybrid algorithm makes it possible to accompany the NPMLE with bootstrap confidence bands.