Kernel estimation of higher derivatives of density and hazard rate function for truncated and censored dependent data

Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function axe given by kernel smoothing method. When observed data exhibit alpha-mixing dependence, local properties including strong consistency and law of iterated logarithm axe 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.