Lognormal kernel estimator of the hazard rate function

Abstract

Estimating the hazard rate function, which is one of the most important ways for representing the lifetime distribution in the survival analysis, has been studied by many researchers. A problem arises when estimating the hazard rate function near the boundary points. This problem is called the boundary bias problem. To solve this problem a variety of techniques have been developed in the literature. One of these techniques is using asymmetric kernels rather than symmetric kernels. In this paper, the lognormal kernel estimator is used to deal with this problem. The asymptotic properties and normality of the lognormal estimation of the density function with nonnegative support and the hazard rate function are established under certain conditions. Also, the selection of the optimal bandwidth is discussed. The performance of the proposed estimator is tested by applications to real-life and simulated data. Also, a comparison of its performance to that of the normal estimator indicates that the lognormal estimator performs better than that of the normal estimator near the boundary.

Keywords:

• Asymptotic mean squared error
• Bias boundary problem
• Kernel estimation
• Lognormal estimator

Acknowledgments

The author would like to thank the referees for helpful suggestions and comments that improve this research.