Efficiency of smoothed distribution function estimator with left truncated and right censored data

A smoothed distribution estimator is proposed when the data are subject to random left truncation and right censorship. The asymptotic properties of the smoothed distribution estimator are established. A relative deficiency is suggested for the smoothed estimator of distribution to the empirical estimator. Under some assumptions, the smoothed distribution estimator is better than the empirical one. In addition, simulation study is conducted and it shows that the smoothed estimator outperforms the empirical one.