We address the empirical bandwidth choice problem in cases where the range of
dependence may be virtually arbitrarily long. Assuming that the observed data derive from
an unknown function of a Gaussian process, it is argued that, unlike more traditional
contexts of statistical inference, in density estimation there is no clear role for the classical
distinction between short-and long-range dependence. Indeed, the" boundaries" that
separate different modes of behaviour for optimal bandwidths and mean squared errors are …