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

Abstract

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

CLC Number:

62G05

CHEN Qing-Beng, DAI Yong-Long. KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA[J].Acta mathematica scientia,Series B, 2003, 23(4): 477-.

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