Asymptotic Behavior of the Hazard Rate Kernel Estimator Under Truncated and Censored Data

Abstract

In this article, we give the asymptotic mean integrated squared error and the mean squared error for the kernel estimator of the hazard rate from truncated and censored data. Martingale techniques and combinatory calculus are used to obtain these results. A probability bound and the optimal bandwidth choice are also given.

Keywords:

• Asymptotic errors
• Hazard rate
• Martingales
• Optimal bandwidth choice
• Truncated and censored data

Mathematics Subject Classification:

• 60G42
• 62F12
• 62G20

Acknowledgment

The authors are grateful to an anonymous referee whose comments gave the way to an improved version of the article.