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
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.