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.
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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.
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Vidal-Sanz, J.M. Automatic spectral density estimation for random fields on a lattice via bootstrap. TEST 18, 96–114 (2009). https://doi.org/10.1007/s11749-007-0059-5
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DOI: https://doi.org/10.1007/s11749-007-0059-5