Spectral density estimation for random fields via periodic embeddings

Joseph Guinness

Biometrika, 2019, vol. 106, issue 2, 267-286

Abstract: SummaryWe introduce methods for estimating the spectral density of a random field on a $d$-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in $O(n\log n)$ time and $O(n)$ memory. However, these so-called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates. In addition, we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias. The paper contains theoretical results on properties of the imputed-data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios. We present an application to a gridded satellite surface temperature dataset with missing values.

Keywords: Circulant embedding; Conjugate gradient; Covariance function; Gaussian process; Nonparametric estimation; Semiparametric estimation; Spatial statistics (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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