A Central Limit Theorem in Non-parametric Regression with Truncated, Censored and Dependent Data

On the basis of the idea of the Nadaraya-Watson (NW) kernel smoother and the technique of the local linear (LL) smoother, we construct the NW and LL estimators of conditional mean functions and their derivatives for a left-truncated and right-censored model. The target function includes the regression function, the conditional moment and the conditional distribution function as special cases. It is assumed that the lifetime observations with covariates form a stationary -mixing sequence. Asymptotic normality of the estimators is established. Finite sample behaviour of the estimators is investigated via simulations. A real data illustration is included too.