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Original Paper

Automatic spectral density estimation for random fields on a lattice via bootstrap

Jose M. Vidal-Sanz¹

(1)	Department of Business Economics, Universidad Carlos III de Madrid, C/ Madrid 126, 28903 Getafe (Madrid), Spain

Received: 27 September 2005 Accepted: 22 March 2007 Published online: 12 May 2007

Abstract We consider the nonparametric estimation of spectral densities for second-order stationary random fields on a d-dimensional lattice. We discuss some drawbacks of standard methods and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. We prove the uniform consistency and study the uniform asymptotic distribution when the optimal smoothing number is estimated from the sampled data.

Keywords Spatial data - Spectral density - Smoothing number - Uniform asymptotic distribution - Bootstrap

Mathematics Subject Classification (2000) 62M30 - 62M15 - 62G20

I wish to thank Professor C. Velasco and two anonymous referees for their helpful comments and suggestions and Professor P.M. Robinson for introducing me with the topic. This research has been supported by a Marie Curie Grant, Mobility 11, of the European Commission, reference number FP6-2004-505469.

Jose M. Vidal-Sanz
Email: jvidal@emp.uc3m.es

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