TY - JOUR
T1 - A generalized measure of uncertainty in geostatistical model selection
AU - Chen, Chun Shu
AU - Zhu, Jun
AU - Chu, Tingjin
N1 - Funding Information:
We thank the Editor, an associate editor, and two referees for their helpful comments and suggestions. We would like to thank Professor Jennifer A. Hoeting for her detailed comments, which have been very helpful in improving the article. The research of Chun-Shu Chen was supported by the Ministry of Science and Technology of Taiwan under Grant MOST 103-2118-M-018-002, the research of Jun Zhu was supported by US Department of Interior USGS CESU Award G16AC00344, and the research of Tingjin Chu was supported by the National Natural Science Foundation of China (grant 11301536).
PY - 2018/1
Y1 - 2018/1
N2 - Model selection and model averaging are essential to regression analysis in environmental studies, 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 (or, instability) 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 analyzed.
AB - Model selection and model averaging are essential to regression analysis in environmental studies, 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 (or, instability) 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 analyzed.
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U2 - 10.5705/ss.202016.0368
DO - 10.5705/ss.202016.0368
M3 - Review article
AN - SCOPUS:85040098506
VL - 28
SP - 203
EP - 228
JO - Statistica Sinica
JF - Statistica Sinica
SN - 1017-0405
IS - 1
ER -