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December 2014 Asymptotic theory of generalized information criterion for geostatistical regression model selection
Chih-Hao Chang, Hsin-Cheng Huang, Ching-Kang Ing
Ann. Statist. 42(6): 2441-2468 (December 2014). DOI: 10.1214/14-AOS1258


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.


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Chih-Hao Chang. Hsin-Cheng Huang. Ching-Kang Ing. "Asymptotic theory of generalized information criterion for geostatistical regression model selection." Ann. Statist. 42 (6) 2441 - 2468, December 2014.


Published: December 2014
First available in Project Euclid: 20 October 2014

zbMATH: 1302.62203
MathSciNet: MR3269985
Digital Object Identifier: 10.1214/14-AOS1258

Primary: 63M30
Secondary: 62F07 , 62F12

Keywords: Akaike’s information criterion , Bayesian Information Criterion , fixed domain asymptotic , increasing domain asymptotic , selection consistency , Variable selection

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 6 • December 2014
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