2019/07/04 by Arthur P. Guillaumin, Adam M. Sykulski, Guillaumin, Arthur P. +5 · 4 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1907.02447
openalex publication_date 2019/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.