Asymptotic normality of the relative error regression function estimator for censored and time series data

Abstract

Consider a survival time study, where a sequence of possibly censored failure times is observed with d-dimensional covariate The main goal of this article is to establish the asymptotic normality of the kernel estimator of the relative error regression function when the data exhibit some kind of dependency. The asymptotic variance is explicitly given. Some simulations are drawn to lend further support to our theoretical result and illustrate the good accuracy of the studied method. Furthermore, a real data example is treated to show the good quality of the prediction and that the true data are well inside in the confidence intervals.

Keywords

• asymptotic normality
• censored data
• kernel smoothing
• probability consistency
• regression function
• relative error
• strong mixing
• 62g05
• 62g08
• 62g30
• 62n01
• 62n02
• 62p10