A bias-correction for cross-validation bandwidth selection when a kernel estimate is based on dependent data

Martin Sköld

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998

ISSN 0281-1944
ISRN LUTFD2/NFMS--3202--SE

Abstract:

Least-squares cross-validation bandwidth selection for kernel density estimation (Rudemo (1982), Bowman(1984)) has been shown to underestimate the optimal bandwidth if data are positively correlated (Hart & Vieu (1990), Sköld (1998)). We calculate the asymptotic bias for the LSCV criterion under a continuous-time model and apply it as a correction term to discrete-time data that can be modeled as a smooth continuous-time process sampled at high rate.

Key words:

non-parametric density estimation, kernel estimate, dependent data, bandwidth selection, cross-validation