A law of the iterated logarithm for error density estimator in censored linear regression

Abstract

We consider the strong consistency of the nonparametric estimation of error density in linear regression with right censored data. The estimator is defined to be the kernel-smoothed estimator of error density, which makes use of the Kaplan-Meier estimator of the error distribution. We establish a point-wise law of the iterated logarithm for kernel-type error density estimator in censored Linear Regression.

Keywords:

• Kaplan-Meier estimator
• right censored data
• bandwidth
• kernel density estimation
• LIL

2010 AMS subject classifications:

• Primary: 62N01
• Secondary: 62N02

Acknowledgements

The author thank a past Editor-in-Chief, an Associate Editor and a reviewer for their valuable comments, which have improved the former version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).