On selection of spatial linear models for lattice data.

On selection of spatial linear models for lattice data.

Zhu, J., Huang, H. and Reyes, P. E.

Journal of the Royal Statistical Society Series B 2010, 72, 389–402. DOI: 10.1111/j.1467-9868.2010.00739.x

ABSTRACT

Spatial linear models are popular for the analysis of data on a spatial lattice, but statistical techniques for selection of covariates and a neighbourhood structure are limited. Here we develop new methodology for simultaneous model selection and parameter estimation via penalized maximum likelihood under a spatial adaptive lasso. A computationally efficient algorithm is devised for obtaining approximate penalized maximum likelihood estimates. Asymptotic properties of penalized maximum likelihood estimates and their approximations are established. A simulation study shows that the method proposed has sound finite sample properties and, for illustration, we analyse an ecological data set in western Canada.

KEYWORDS: Conditional auto-regressive model; Model selection; Penalized likelihood; Simultaneous auto-regressive model; Spatial statistics; Variable selection.