On the estimation of the spectral density for continuous spatial processes

Abstract

In this work, we study the asymptotic properties of smoothed nonparametric kernel spectral density estimators for the spatial spectral density. We consider the case of continuous stationary spatial processes under a shrinking asymptotic framework. Expressions for the bias and the covariance structure are obtained and the implications for the edge effect bias of the choice of the kernel, bandwidth and spacing parameter in the design are also discussed, both for tapered and untapered estimates. Results are illustrated with a simulation study.

Keywords:

• spatial spectral density
• continuous spatial process
• nonparametric estimation
• periodogram
• edge-effect
• tapering

AMS Subject Classification :

• 62M30
• 62M15
• 62G05

Acknowledgements

The authors want to thank Prof. Peter Robinson and Prof. Wenceslao González-Manteiga for their help. We also thank an anonymous referee for the helpful comments. Part of this work has been done during a stage in London School of Economics. This work has been supported by project MTM2008-0310 of the Ministry of Education and Science. R.M.C. has also received funds from project Xunta de Galicia PGIDIT06PXIB207009PR and grant BES2003-0581.