On the asymptotic mean integrated squared error of a kernel density estimator for dependent data

Abstract

Hall and Hart (1990) proved that the mean integrated squared error (MISE) of a marginal kernel density estimator from an infinite moving average process X 1, X 2, … may be decomposed into the sum of MISE of the same kernel estimator for a random sample of the same size and a term proportional to the variance of the sample mean. Extending this, we show here that the phenomenon is rather general: the same result continues to hold if dependence is quantified in terms of the behaviour of a remainder term in a natural decomposition of the densities of ( X 1, X 1+ i ), i = 1, 2, ….