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On selection of spatial linear models for lattice data

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

Document Type: Research Article

Affiliations: 1: Colorado State University, Fort Collins, and University of Wisconsin, Madison, USA 2: Academia Sinica, Taipei, and National Chiao Tung University, Hsinchu, Taiwan 3: University of Wisconsin, Madison, USA

Publication date: 01 June 2010

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