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Statistica Sinica 20 (2010), 871-910





A GENERAL ASYMPTOTIC THEORY FOR MAXIMUM

LIKELIHOOD ESTIMATION IN SEMIPARAMETRIC

REGRESSION MODELS WITH CENSORED DATA


Donglin Zeng and D. Y. Lin


University of North Carolina at Chapel Hill


Abstract: We establish a general asymptotic theory for nonparametric maximum likelihood estimation in semiparametric regression models with right censored data. We identify a set of regularity conditions under which the nonparametric maximum likelihood estimators are consistent, asymptotically normal, and asymptotically efficient with a covariance matrix that can be consistently estimated by the inverse information matrix or the profile likelihood method. The general theory allows one to obtain the desired asymptotic properties of the nonparametric maximum likelihood estimators for any specific problem by verifying a set of conditions rather than by proving technical results from first principles. We demonstrate the usefulness of this powerful theory through a variety of examples.



Key words and phrases: Counting process, empirical process, multivariate failure times, nonparametric likelihood, profile likelihood, survival data.

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