Kernel estimation of conditional density with truncated, censored and dependent data

Abstract

In this paper we define a kernel estimator of the conditional density for a left-truncated and right-censored model based on the generalized product-limit estimator of the conditional distributed function. Under the observations with multivariate covariates form a stationary α-mixing sequence, we derive the asymptotic normality as well as a Berry–Esseen type bound for the proposed estimator. Also, the uniform convergence with rates for the estimator is considered. Finite sample behavior of the estimator is investigated via simulations too.