Nonparametric conditional hazard rate estimation: A local linear approach

Abstract

A new nonparametric estimator for the conditional hazard rate is proposed, which is defined as the ratio of local linear estimators for the conditional density and survivor function. The resulting hazard rate estimator is shown to be pointwise consistent and asymptotically normally distributed under appropriate conditions. Furthermore, plug-in bandwidths based on normal and uniform reference distributions and minimizing the asymptotic mean squared error are derived. In terms of the mean squared error the new estimator is highly competitive in comparison to existing estimators for the conditional hazard rate. Moreover, its smoothing parameters are relatively robust to misspecification of the reference distributions, which facilitates bandwidth selection. Additionally, the new hazard rate estimator is conveniently calculated using standard software for local linear regression. The use of the local linear hazard rate is illustrated in an application to kidney transplant data.