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 strictly stationary continuous time process observed over the time interval [0, T], it is necessary to have at oneʹs disposal a Central Limit Theorem for the kernel density estimator fT. In this paper we address the question of nonparametric estimation of the asymptotic variance of T fT, an unknown quantity dependent on f. We construct two estimators and study their asymptotic properties.