One-Step Estimation of Spatial Dependence Parameters: Properties and Extensions of the APLE Statistic

We consider one-step estimation of parameters that represent the strength of spatial dependence in a geostatistical or lattice spatial model. While the maximum likelihood estimators (MLE) of spatial dependence parameters are known to have various desirable properties, they do not have closed-form expressions. Therefore, we consider a one-step alternative to maximum likelihood estimation based on solving an approximate (i.e., one-step) profile likelihood estimating equation. The resulting approximate profile likelihood estimator (APLE) has a closed-form representation, making it a suitable alternative to the widely used Moran’s I statistic. Since the finite-sample and asymptotic properties of one-step estimators of covariance-function parameters have not been studied rigorously, we explore these properties for the APLE of the spatial dependence parameter in the simultaneous autoregressive (SAR) model. In addition, we develop exploratory spatial data analysis tools based on this APLE statistic, which capture regions of local clustering or the extent to which the strength of spatial dependence varies across space. These tools are illustrated using both simulated data and observed crime rates in Columbus, OH.

By: Hongfei Li; Catherine A. Calder; Noel Cressie

Published in: Journal of Multivariate Analysis, volume 105, (no 1), pages 68-84 in 2012

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