ABSTRACT
The computation of the empirical likelihood ratio is closely related to the computation of the nonparametric maximum likelihood estimators (NPMLE) and the constrained NPMLE. For right-censored data, the NPMLE of the CDF is the Kaplan–Meier estimator and the NPMLE of the cumulative hazard function is the Nelson–Aalen estimator, which are both explicitly given and easy to compute. The constrained versions of NPMLE usually do not have an explicit formula and are harder to calculate. We discuss in this Chapter several methods and the related issues in computing the constrained Kaplan–Meier and Nelson–Aalen estimators and the related empirical likelihood ratios. The methods include the Newton type iteration, Lagrange multiplier technique, sequential quadratic programming, and expectation-maximization (EM) algorithm. Their implementation in R is also discussed.
