On computation of semiparametric maximum likelihood estimators with shape constraints.

Large sample theory of semiparametric models based on maximum likelihood estimation (MLE) with shape constraint on the nonparametric component is well studied. Relatively less attention has been paid to the computational aspect of semiparametric MLE. The computation of semiparametric MLE based on existing approaches such as the expectation-maximization (EM) algorithm can be computationally prohibitive when the missing rate is high. In this paper, we propose a computational framework for semiparametric MLE based on an inexact block coordinate ascent (BCA) algorithm. We show theoretically that the proposed algorithm converges. This computational framework can be applied to a wide range of data with different structures, such as panel count data, interval-censored data, and degradation data, among others. Simulation studies demonstrate favorable performance compared with existing algorithms in terms of accuracy and speed. Two data sets are used to illustrate the proposed computational method. We further implement the proposed computational method in R package BCA1SG, available at CRAN.