Divergence-based Inference for Autoregressive Process Indexed by Regular Lattice

Pramita Bagchi

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and Anand N. Vidyashankar

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${}^{1}$

Department of Biostatistics & Bioinformatics, George Washington University, Washington, DC, USA [pramita.bagchi@gwu.edu]
${}^{2}$

Department of Statistics, George Mason University, Fairfax, VA, USA [avidyash@gmu.edu]

Keywords: Spatial – Spatio-temporal – SAR – Divergence – Robustness

Simultaneous autoregressive (SAR) processes are valuable and popular in modeling various spatial and spatio-temporal data arising in various fields, including environmental science, ecology, and medical imaging. In this presentation, we propose a divergence-based inferential framework for the parameters of a causal SAR process in general dimension. We derive the asymptotic properties of the minimum divergence estimators and establish efficiency when the posited model is correct. Like other minimum divergence estimators, these estimators are more robust to departures from the model assumptions compared to standard likelihood-based methods. We also study the performance of the proposed methods with extensive numerical simulations and real-world data.