The asymptotic variance of the continuous-time kernel estimator with applications to bandwidth selection

Martin Sköld

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

ISSN 0281-1944

We derive simple expressions for the asymptotic variance of the kernel density estimator of a stationary continuous-time process in one and d dimensions and relate convergence rates to sample path smoothness. The results are applied to bandwidth selection for discrete-time process that can be modeled as dense samples from smooth continuous-time processes.
Key words:
nonparametric density estimation, kernel estimate, dependent data, continuous time, bandwidth selection