Some inequalities for the kernel density estimator under random censorship^∗

^∗Research Supported by the National Natural Science Foundation of China.

Abstract

In this paper, the kernel density estimator proposed by Blum and Susarla (1980) is investigated. Three inequalities, a L₁ error inequality, a pth, p>=2, order absolute moment inequality and a probability inequality, are established, respectively.

Keywords:

• Kernel density estimator
• L₁ -moment inequality
• random censorship

AMS 1991 Subject Classifications:

• Primary: 62G05
• Secondary: 62E20

^∗Research Supported by the National Natural Science Foundation of China.

^∗Research Supported by the National Natural Science Foundation of China.

Notes

^∗Research Supported by the National Natural Science Foundation of China.