On the asymptotic variance of the continuous-time kernel density estimator

Martin Sköld and Ola Hössjer

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

We reformulate the conditions of Blanke & Bosq (1997)  for achieving the log(T)/T-rate of convergence of the kernel density estimator for a smooth process and give under slightly stronger assumptions the exact asymptotic form of the variance giving an expression for the asymptotic optimal bandwidth. Conditions for the full 1/T and discrete-time rates are also considered.