Penalized Whittle likelihood for spatial data

Kun Chen, Ngai Hang Chan, Chun Yip Yau and Jie Hu

Journal of Multivariate Analysis, 2023, vol. 195, issue C

Abstract: Inference for spatial data is challenging because fitting an appropriate parametric model is often difficult. The penalized likelihood-type approach has been successfully developed for various nonparametric function estimation problems in time series analysis. However, it has not been well developed in spatial analysis. In this paper, a penalized Whittle likelihood approach is developed for nonparametric estimation of spectral density functions for regularly spaced spatial data. In particular, the estimated spectral density is the minimizer of a criterion which is developed based on the Whittle likelihood and a penalty for roughness. This approach aggregates several popular nonparametric density estimation methods into a coherent framework. Asymptotic properties of the proposed estimator are derived under mild assumptions without assuming Gaussianity. In addition, a computationally efficient method is developed to optimize the penalized likelihood function. Simulation results and real data examples are also provided to illustrate the finite sample performances of the methodology.

Keywords: Adaptive smoothing; Frequency domain; Regularization; Spatial lattice data; Spatial periodogram (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2023.105156

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