Sieve least squares estimator for partial linear models with current status data

Abstract

Current status data often arise in survival analysis and reliability studies, when a continuous response is reduced to an indicator of whether the response is greater or less than an observed random threshold value. This article considers a partial linear model with current status data. A sieve least squares estimator is proposed to estimate both the regression parameters and the nonparametric function. This paper shows, under some mild condition, that the estimators are strong consistent. Moreover, the parameter estimators are normally distributed, while the nonparametric component achieves the optimal convergence rate. Simulation studies are carried out to investigate the performance of the proposed estimates. For illustration purposes, the method is applied to a real dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract treatment.