The Debiased Spatial Whittle likelihood

• 成果类型: Article
• 署名作者: Guillaumin, Arthur P.; Sykulski, Adam M.; Olhede, Sofia C.; Simons, Frederik J.
• 署名单位: University of London; Queen Mary University London; Lancaster University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of London; University College London; Princeton University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12539
• 发表日期: 2022
• 页码: 1526-1557
• 关键词: parameter-estimation; stationary process; time-series; covariance; models

摘要

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 generalize 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(nlogn) 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 realworld 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.