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 α‐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.