Nonparametric estimators are proposed for transition probabilities in partial Markov chains relative to multiple decrement models. The estimators are generalizations of the product limit estimator. We study the bias of the estimators, prove a strong consistency result and derive asymptotic normality of the estimators considered as stochastic processes. We also compute their efficiency relative to the maximum likelihood estimators in the case of constant forces of transition.
"Nonparametric Estimation of Partial Transition Probabilities in Multiple Decrement Models." Ann. Statist. 6 (3) 534 - 545, May, 1978. https://doi.org/10.1214/aos/1176344198