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April 1999 Asymptotically optimal estimation of smooth functionals for interval censoring, case $2$
Ronald Geskus, Piet Groeneboom
Ann. Statist. 27(2): 627-674 (April 1999). DOI: 10.1214/aos/1018031211


For a version of the interval censoring model, case 2, in which the observation intervals are allowed to be arbitrarily small, we consider estimation of functionals that are differentiable along Hellinger differentiable paths. The asymptotic information lower bound for such functionals can be represented as the squared $L_{2}$-norm of the canonical gradient in the observation space. This canonical gradient has an implicit expression as a solution of an integral equation that does not belong to one of the standard types. We study an extended version of the integral equation that can also be used for discrete distribution functions like the nonparametric maximum likelihood estimator (NPMLE) , and derive the asymptotic normality and efficiency of the NPMLE from properties of the solutions of the integral equations.


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Ronald Geskus. Piet Groeneboom. "Asymptotically optimal estimation of smooth functionals for interval censoring, case $2$." Ann. Statist. 27 (2) 627 - 674, April 1999.


Published: April 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0954.62034
MathSciNet: MR1714713
Digital Object Identifier: 10.1214/aos/1018031211

Primary: 45A05, 60F17, 62E20, 62G05, 62G20

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 2 • April 1999
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