Asymptotic Behaviors of Conditional Generalized Information Criterion for Geostatistical Regression Model Selectio

Abstract

Conditional Akaike's information criterion is usually applied in model selection for prediction purpose which is of main interest in geostatisitcs. In our research, we consider a squared error loss function and show that a model independent lower bounded of the loss function is possibly to be a dominant term by slowing down the growing rate of the observation domain. We establish the asymptotic loss/risk efficiency of CAIC under some regularity conditions. However, model selection may improve none to the asymptotic loss/risk efficiency in some cases because of the dominant term of SPE. In this talk, we modify the loss function by dropping the dominant term and then establish the corresponding asymptotic theory of conditional generalized information criterion (CGIC) which includes CAIC as a special case. Keywords：variable selection, fixed domain asymptotics, Conditional GIC