Complete second moment convergence rate property estimator under a general censoring model

Abstract

This work uses a new mode of convergence, called complete second moments convergence which represents an innovation in the study of convergences with rates. It implies the rates of other types of convergence such as almost complete convergence and mean square error convergence. The advantage of this mode is that it improves the rates obtained using these two types of convergence. In addition to showing this property on the asymptotic efficiency of the estimator, we propose a new nonparametric estimator of the conditional density function based on the use of two kernels applied to the conditional variables, where the observations are subject to a general censorship including left, right, double and twice censoring.