2014/10/20 by Chih-Hao Chang, Chih‐Hao Chang, Hsin‐Cheng Huang +3
Engineering · Environmental Science · Mathematics · #Akaike information criterion #Applied mathematics #Asymptotic analysis #Bayesian information criterion #Bounded function #Computer science #Consistency (knowledge bases) #Covariance #Information Criteria #Mathematical analysis #Mathematics #Mineral Processing and Grinding #Model selection #Selection (genetic algorithm) #Smoothness #Soil Geostatistics and Mapping #Statistical Methods and Inference #Statistics #math.ST #stat.TH
paper · pdf · doi:10.1214/14-aos1258
published as Annals of Statistics 2014, Vol. 42, No. 6, 2441-2468 · Published in at http://dx.doi.org/10.1214/14-AOS1258 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2014/10/20 · arxiv created 2014/12/02 · arxiv updated 2014/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Information criteria, such as Akaike’s information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region. In this article, we study the generalized information criterion (GIC) for selecting geostatistical regression models under a more general mixed domain asymptotic framework. Via uniform convergence developments of some statistics, we establish the selection consistency and the asymptotic loss efficiency of GIC under some regularity conditions, regardless of whether the covariance model is correctly or wrongly specified. We further provide specific examples with different types of explanatory variables that satisfy the conditions. For example, in some situations, GIC is selection consistent, even when some spatial covariance parameters cannot be estimated consistently. On the other hand, GIC fails to select the true polynomial order consistently under the fixed domain asymptotic framework. Moreover, the growth rate of the domain and the degree of smoothness of candidate regressors in space are shown to play key roles for model selection.