Asymptotically Optimal Estimation of Smooth Functionals for Interval Censoring,Case 2

摘要

For the interval censoring model, case 2, we consider estimation of functionalsthat are differentiable along Hellinger differentiable paths. The asymptotic information lower bound for such functionals can be represented as an L2-inner product of two functions. One is the derivative of the canonical gradient of the functional if there would be no censoring. The other one occurs in the canonical gradient expression in the censoring model, and has an implicit expression as solution of an integral equation that does not belong to one of the standard types. We study the situation in which the observation times can become arbitrarily close to each other. Properties of the solution to the integral equation are derived and asymptotic efficiency of the nonparametric maximum likelihood estimator is established.