Weighted estimation of conditional mean function with truncated, censored and dependent data

Abstract

By applying the empirical likelihood method, we construct a new weighted estimator of the conditional mean function for a left-truncated and right-censored model. Assuming that the observations form a stationary α-mixing sequence, we derive weak convergence with a certain rate and prove asymptotic normality of the weighted estimator. The asymptotic normality shows that the weighted estimator preserves the bias, variance, and, more importantly, automatic good boundary behavior of a local linear estimator of the conditional mean function. Also, a Berry-Esseen type bound for the weighted estimator is established. A simulation study is conducted to study the finite sample behavior of the new estimator and a real data application is provided.