Asymptotic Theory for Geostatistical Model Selection

• Main Authors: Chang, Chih-Hao, 張志浩
• Other Authors: Huang, Hsin-Cheng
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/80000963500140399576

博士 === 國立交通大學 === 統計學研究所 === 99 === Information criteria, such as Akaike's information criterion (AIC), Bayesian information criterion (BIC), and conditional AIC (CAIC) are often applied in model selection. However, their asymptotic behaviors under 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 thesis, we investigate two classes of criteria for geostatistical model selection: generalized information criterion (GIC) and conditional GIC (CGIC), which include AIC, BIC, and CAIC as special cases, under both the increasing domain asymptotic and fixed domain asymptotic frameworks. We establish conditions under which GIC and CGIC are selection consistent and asymptotically efficient even without assuming spatial covariance structure to be known. These conditions are further examined for GIC and CGIC in selecting one-dimensional geostatistical regression models with the exponential covariance function class under various settings. For example, under the fixed domain asymptotic framework, where some covariance parameters are not consistently estimable, we show that selection consistency not only depends on the tuning parameter of GIC, but also depends on smoothness of the explanatory variables in space. In addition, under the increasing domain framework, we show that asymptotic properties of GIC depend on the growing rates for the size of the domain. Moreover, some numerical experiments are provided to demonstrate the finite sample behavior of various criteria.