Variable Bandwidths for Nonparametric Hazard Rate Estimation

Abstract

A smoothing parameter inversely proportional to the square root of the true density is known to produce kernel estimates of the density having faster bias rate of convergence. We show that in the case of kernel-based nonparametric hazard rate estimation, a smoothing parameter inversely proportional to the square root of the true hazard rate leads to a mean square error rate of order n ^−8/9, an improvement over the standard second order kernel. An adaptive version of such a procedure is considered and analyzed.

Keywords:

• Hazard rate estimation
• Kernel
• Mean integrated square error
• Smoothness
• Variable bandwidth

Mathematics Subject Classification:

• Primary 62G05, 62N02
• Secondary 62P10, 62G30

Acknowledgment

The authors would like to thank the referees for helpful suggestions and comments that lead to improvements of this research.