数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (4): 477-.

• 论文 • 上一篇    下一篇

KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA

 陈清平, 戴永隆   

  1. 1.Department of Statistics, Wuhan University, Wuhan 430072, China
    2.Wuhan University of Science and Technology, Wuhan 430081, China
    3.Department of Statistics, Zhongshan University, Guangzhou 510275, China
  • 出版日期:2003-10-06 发布日期:2003-10-06

KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA

 CHEN Qing-Beng, DAI Yong-Long   

  1. 1.Department of Statistics, Wuhan University, Wuhan 430072, China
    2.Wuhan University of Science and Technology, Wuhan 430081, China
    3.Department of Statistics, Zhongshan University, Guangzhou 510275, China
  • Online:2003-10-06 Published:2003-10-06

摘要:

Based on left truncated and right censored dependent data, the estimators
of higher derivatives of density function and hazard rate function are given by kernel
smoothing method. When observed data exhibit -mixing dependence, local properties
including strong consistency and law of iterated logarithm are presented. Moreover, when
the mode estimator is defined as the random variable that maximizes the kernel density
estimator, the asymptotic normality of the mode estimator is established.

关键词: Truncated and censored data, -mixing, strong consistency, law of iterated logarithm, mode

Abstract:

Based on left truncated and right censored dependent data, the estimators
of higher derivatives of density function and hazard rate function are given by kernel
smoothing method. When observed data exhibit -mixing dependence, local properties
including strong consistency and law of iterated logarithm are presented. Moreover, when
the mode estimator is defined as the random variable that maximizes the kernel density
estimator, the asymptotic normality of the mode estimator is established.

Key words: Truncated and censored data, -mixing, strong consistency, law of iterated
logarithm, mode

中图分类号: 

  • 62G05