Bandwidth Selection Problem for Nonparametric Regression Model with Right-Censored Data

Abstract

In this paper, the proposed estimator for the unknown nonparametric regression function is a Nadarya-Watson (Nadarya, 1964; Watson, 1964) type kernel estimator. In this estimation procedure, the censored observations are replaced by synthetic data points based on Kaplan-Meier estimator. As known performance of the kernel estimator depends on the selection of a bandwidth parameter. To get an optimum parameter we have considered six selection methods such as the improved version of Akaike information criterion (AICc), Bayesian information criterion (BIC), generalized cross validation (GCV), risk estimation with classical pilots (RECP), Mallow’s Cp criterion and restricted empirical likelihood (REML), respectively. In addition, we discuss the behavior of the estimators obtained by these selection methods under different configurations of the censoring level and sample sizes. Simulation and real lifetime data results are presented to evaluate and compare the performance of the selection methods. Thus, a optimum criterion is provided for smoothing parameter selection.

Keywords

• Kernel Smoothing
• Kaplan-Meier Estimator
• Nonparametric Regression
• Censored data