Feasible pairwise pseudo-likelihood inference on spatial regressions in irregular lattice grids: the KD-T PL algorithm

TL;DR

This paper introduces a KD-tree based algorithm to efficiently compute pairwise pseudo-likelihood estimations for spatial error models on large, irregular grids, significantly reducing computational costs while maintaining accuracy.

Contribution

The paper presents a novel KD-tree based algorithm that streamlines pairwise likelihood estimation for spatial regressions on irregular grids, improving computational efficiency.

Findings

Significant reduction in computation time compared to full likelihood methods.

Maintains estimation accuracy despite computational simplifications.

Effective application demonstrated on simulated spatial data.

Abstract

Spatial regression models are central to the field of spatial statistics. Nevertheless, their estimation in case of large and irregular gridded spatial datasets presents considerable computational challenges. To tackle these computational problems, Arbia \citep{arbia_2014_pairwise} introduced a pseudo-likelihood approach (called pairwise likelihood, say PL) which required the identification of pairs of observations that are internally correlated, but mutually conditionally uncorrelated. However, while the PL estimators enjoy optimal theoretical properties, their practical implementation when dealing with data observed on irregular grids suffers from dramatic computational issues (connected with the identification of the pairs of observations) that, in most empirical cases, negatively counter-balance its advantages. In this paper we introduce an algorithm specifically designed to streamline the computation of the PL in large and irregularly gridded spatial datasets, dramatically simplifying the estimation phase. In particular, we focus on the estimation of Spatial Error models (SEM). Our proposed approach, efficiently pairs spatial couples exploiting the KD tree data structure and exploits it to derive the closed-form expressions for fast parameter approximation. To showcase the efficiency of our method, we provide an illustrative example using simulated data, demonstrating the computational advantages if compared to a full likelihood inference are not at the expenses of accuracy.