Spectral density estimation for random fields via periodic embeddings. (3rd April 2019)

• Record Type: Journal Article
• Authors: Guinness, Joseph
• Is Part Of: Biometrika. Volume 106:Number 2(2019:Jun.)
• Page Start: 267
• Page End: 286
• Publication Date: 2019-04-03
• Subjects: Circulant embedding -- Conjugate gradient -- Covariance function -- Gaussian process -- Nonparametric estimation -- Semiparametric estimation -- Spatial statistics; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asz004
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: We 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.