Measuring stabilization in model selection

Chun-Shu Chen

Institute of Statistics and Information Science

National Changhua University of Education

cschen@cc.ncue.edu.tw

    Model selection and model averaging are essential to regression analysis, but determining which of the two approaches is the more appropriate and under what circumstances remains an active research topic. In this paper, we focus on geostatistical regression models for spatially referenced environmental data. For a general information criterion, we develop a new perturbation-based criterion that measures the uncertainty of spatial model selection, as well as an empirical rule for choosing between model selection and model averaging. Statistical inference based on the proposed model selection instability measure is justified both in theory and via a simulation study. The predictive performance of model selection and model averaging can be quite different when the uncertainty in model selection is relatively large, but the performance becomes more comparable as this uncertainty decreases. For illustration, a precipitation data set in the state of Colorado is analysed. This is a joint work with Jun Zhu and Tingjin Chu.

Keyword: Information criterion, model complexity, spatial prediction