Selection of spatial and spatial-temporal linear models for lattice data

Spatial linear models are popular for the analysis of data on a spatial lattice, but statistical techniques for selection of covariates and a neighborhood structure are limited. This thesis develops new methodology for simultaneous model selection and parameter estimation via penalized maximum likelihood under a spatial adaptive Lasso penalty. 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 proposed method has sound finite-sample properties and for illustration, an ecological data set is analyzed.;Further, linear regression is considered for the analysis of spatial lattice data repeatedly measured over time. In particular, the impact of temperature, precipitation, and elevation on the tree-killing ability of an eruptive species of bark beetle in pine forests of British Columbia, Canada is evaluated. The methodology for simultaneous spatial model selection and parameter estimation is extended to spatial-temporal modeling. The approach is again penalized maximum likelihood estimation but under a spatial-temporal adaptive Lasso penalty. A computationally efficient algorithm is devised for obtaining approximate penalized maximum likelihood estimates. The new method is applied to analyze landscape-level spatial-temporal lattice data in the bark beetle study and the results are interpreted from ecological perspectives. Asymptotic properties of penalized maximum likelihood estimates and their approximations are established and finite-sample properties are studied in a simulation study.