Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 99, Issue 466, Pages 346-356Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/016214504000000313
Keywords
asymptotically efficient estimator; maximum likelihood estimator; optimal convergence rate; partial linear model; strongly consistent
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In a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event, it is often too expensive or even impossible to observe the exact time. However, the current status of the subject at a random time of inspection is much more natural, feasible, and practical in terms of cost-effectiveness. This article considers a semiparametric regression model that consists of parametric and nonparametric regression components. A sieve maximum likelihood estimator (MLE) is proposed to estimate the regression parameter, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically efficient and normally distributed, and the estimator of the nonparametric function has an optimal convergence rate. Simulation Studies were carried out to investigate the performance of the proposed method. For illustration purposes, the method is applied to a dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract treatment.
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