Strong consistency of the nonparametric local linear regression estimation under censorship model

Abstract

We introduce and study a local linear nonparametric regression estimator for censorship model. The main goal of this paper is, to establish the uniform almost sure consistency result with rate over a compact set for the new estimate. To support our theoretical result, a simulation study has been done to make comparison with the classical regression estimator.

Keywords:

• Censored data
• local linear estimation
• rate of consistency
• regression function
• survival analysis
• uniform almost sure consistency

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62G05
• 62G08
• 62G20

Acknowledgments

The authors are grateful to an anonymous referee whose careful reading gave them the opportunity to improve the quality of the paper and add a pointwise strong consistency result without rate under weak conditions.