Estimation of the asymptotic variance of kernel density estimators for continuous time processes

In order to construct confidence sets for a marginal density f of a strictl y stationary continuous time process observed over the time interval [0, T] , it is necessary to have at one's disposal a Central Limit Theorem for the kernel density estimator f(T) . In this paper we address the question of n onparametric estimation of the asymptotic variance of rootT f(T) an unknown quantity dependent on f. We construct two estimators and study their asymp totic properties, (C) 2001 Academic Press.