Locally Eecient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curse of dimensionality it is typically not possible to construct estimators which are asymptotically eecient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators which are eecient at a chosen submodel of the full-data model, are still well behaved oo this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem which provides a template for proving the wished asymptotic results. We illustrate the general one-step estimation method by constructing locally eecient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covari-ates. The conditions of the asymptotics theorem are rigorously veriied in one of the examples and the key condition of the general theorem is veriied for all examples.