Comparing composite likelihood methods based on pairs for spatial Gaussian random fieldsM

TL;DR

This paper compares pairwise composite likelihood methods for estimating covariance functions in large spatial Gaussian datasets, analyzing their efficiency and computational trade-offs through theory, simulations, and real data.

Contribution

It introduces and evaluates three weighted pairwise composite likelihood methods and compares them with covariance tapering, highlighting their statistical and computational performance.

Findings

All methods provide consistent estimates.

Trade-offs observed between efficiency and computational speed.

Composite likelihood methods are viable alternatives to maximum likelihood for large datasets.

Abstract

In the last years there has been a growing interest in proposing methods for estimating covariance functions for geostatistical data. Among these, maximum likelihood estimators have nice features when we deal with a Gaussian model. However maximum likelihood becomes impractical when the number of observations is very large. In this work we review some solutions and we contrast them in terms of loss of statistical efficiency and computational burden. Specifically we focus on three types of weighted composite likelihood functions based on pairs and we compare them with the method of covariance tapering. Asymptotics properties of the three estimation methods are derived. We illustrate the effectiveness of the methods through theoretical examples, simulation experiments and by analysing a data set on yearly total precipitation anomalies at weather stations in the United States.