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

摘要

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