The debiased spatial Whittle likelihood
File(s)
Published version
OA Location
Author(s)
Guillaumin, Arthur P
Sykulski, Adam M
Olhede, Sofia C
Simons, Frederik J
Type
Journal Article
Abstract
We provide a computationally and statistically efficient method for
estimating the parameters of a stochastic covariance model observed on a
regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle likelihood to account for large sources of bias caused by boundary effects and aliasing. We generalise the approach to flexibly allow for significant volumes of missing data including those with lower-dimensional substructure, and for irregular sampling boundaries. We build a theoretical framework under relatively weak assumptions which ensures consistency and asymptotic normality in numerous practical settings including missing data and non-Gaussian processes. We also extend our consistency results to multivariate processes. We provide detailed implementation guidelines which ensure the estimation procedure can be conducted in O(n log n) operations, where n is the number of points of the encapsulating rectangular grid, thus keeping the computational scalability of Fourier and Whittle-based methods for large data sets. We validate our procedure over a range of simulated and real-world settings, and compare with state-of-the-art alternatives, demonstrating the enduring practical appeal of Fourier-based methods, provided they are corrected
by the procedures developed in this paper.
estimating the parameters of a stochastic covariance model observed on a
regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle likelihood to account for large sources of bias caused by boundary effects and aliasing. We generalise the approach to flexibly allow for significant volumes of missing data including those with lower-dimensional substructure, and for irregular sampling boundaries. We build a theoretical framework under relatively weak assumptions which ensures consistency and asymptotic normality in numerous practical settings including missing data and non-Gaussian processes. We also extend our consistency results to multivariate processes. We provide detailed implementation guidelines which ensure the estimation procedure can be conducted in O(n log n) operations, where n is the number of points of the encapsulating rectangular grid, thus keeping the computational scalability of Fourier and Whittle-based methods for large data sets. We validate our procedure over a range of simulated and real-world settings, and compare with state-of-the-art alternatives, demonstrating the enduring practical appeal of Fourier-based methods, provided they are corrected
by the procedures developed in this paper.
Date Issued
2022-09-01
Date Acceptance
2022-03-04
Citation
Journal of the Royal Statistical Society Series B: Statistical Methodology, 2022, 84 (4), pp.1526-1557
ISSN
1369-7412
Publisher
Wiley
Start Page
1526
End Page
1557
Journal / Book Title
Journal of the Royal Statistical Society Series B: Statistical Methodology
Volume
84
Issue
4
Copyright Statement
© 2022 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
https://rss.onlinelibrary.wiley.com/doi/full/10.1111/rssb.12539
Subjects
stat.AP
stat.CO
stat.ME
stat.ME
stat.ML
Publication Status
Published
Date Publish Online
2022-07-20