A Hybrid Algorithm for Computation of the Nonparametric Maximum Likelihood Estimator from Censored Data

Abstract

We present a hybrid algorithm for nonparametric maximum likelihood estimation from censored data when the log-likelihood is concave. The hybrid algorithm uses a composite algorithmic mapping combining the expectation-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) unambiguously. Numerical simulations demonstrate that the hybrid algorithm converges more rapidly than either of the EM or the naive ICM algorithm for doubly censored data. The speed of the hybrid algorithm makes it possible to accompany the NPMLE with bootstrap confidence bands.

Key Words:

• Algorithm
• Censoring
• EM algorithm
• Hybrid method
• Iterative convex minorant
• Missing data
• Self-consistency