Asymptotic distribution of data‐driven smoothers in density and regression estimation under dependence

Abstract
We consider automatic data‐driven density, regression and autoregression estimates, based on any random bandwidth selector h/T. We show that in a first‐order asymptotic approximation they behave as well as the related estimates obtained with the “optimal” bandwidthhTas long ashT/hT→ 1 in probability. The results are obtained for dependent observations; some of them are also new for independent observations.