On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models

Abstract

Estimating hazard rate function is an important problem in survival analysis. There are some estimation approaches based on kernel smoothing. However, they suffer from the boundary effects or need high order kernels, which increases the mean squared error. We introduce local polynomial estimators of hazard rates and their derivatives for the left truncation and right censoring models. The estimators have favorable properties similar to those of local polynomial regression estimators. Asymptotic expressions for the mean squared errors (AMSE's) are obtained. Consistency and joint asymptotic normality of the local polynomial estimators are established. A data-based local bandwidth selection rule is proposed. X X On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models 200 Copyright: ©2018 Jiang et al. Citation: Jiang J, Chen L, Yuan Y. On local polynomial estimation of hazard rates and their derivatives under left truncation and right censoring models.