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

Abstract

This paper considers the nonparametric estimation of spectral densities for second order stationary random fields on a d-dimensional lattice. I 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. I prove 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. AMS 2000 subject classifications:. Primary 62M30; secondary 62M15, 62G20 * A version of this paper is published in TEST, by Springer Verlag, DOI 10.1007/s11749-007-0059-5. 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 in the topic.

Autoregressive spatial spectral estimates

“…Yuan and Subba Rao (1993), Politis and Romano (1996), Robinson (2007) and Vidal Sanz (2009). Our autoregressive approach allows us to consider nonparametric estimates of the spectral density without the practitioner having to choose a taper or kernel.…”

Exploring spectral density estimation for spatial linear process with mixing innovations

“…Some recent papers deal with spatial periodogram smoothing but there is no work concerning weak processes. Different filters are used in literature, see, for example, [19] which focuses on kernel estimator of spectral density, with optimal smoothing number estimated from the data. The author studied consistency and asymptotic distribution of this estimator, with an automatic estimate of this smoothing number.…”