B0633
Title: Efficient and accurate estimation from dependent data: The debiased spatial Whittle likelihood
Authors: Sofia Olhede - EPFL (Switzerland) [presenting]
Adam Sykulski - Imperial College London (United Kingdom)
Arthur Guillaumin - Queen Mary University of London (United Kingdom)
Frederik Simons - Princeton (United States)
Abstract: A computationally and statistically efficient method is proposed 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(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 it with state-of-the-art alternatives, demonstrating the enduring practical appeal of Fourier-based methods, provided they are corrected by the developed procedures.