Asymptotic Theory of Generalized Information Criterion for Geostatistical Regression Model Selection

Abstract

Model selection is well studied in statistics which is generally applied by some information criteria, such as Akaike's information criterion and Bayesian information criterion. 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. This talk aims introducing 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. Some examples are given at the end of this talk, in which we show some non-standard behaviors of GIC under the fixed domain asymptotic framework.?