A general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood. Conditions are given for consistency and asymptotic normality, and a method is provided for the calculation of the asymptotic efficiency of the estimator. The implications of the general theory are examined in special cases such as inference in stochastic processes, Cox regression models, and AR processes with missing segments.
"Theory of Partial Likelihood." Ann. Statist. 14 (1) 88 - 123, March, 1986. https://doi.org/10.1214/aos/1176349844