标题： 地理统计回归模型选择的广义信息准则的渐近理论 显示英文标题

标题： Asymptotic theory of generalized information criterion for geostatistical regression model selection

摘要： 信息准则，如赤池信息量准则和贝叶斯信息准则，常用于模型选择。然而，它们在选择地质统计回归模型时的渐近行为尚未得到充分研究，特别是在固定域渐近框架下，随着越来越多的数据在一个有界的固定区域内被观测到的情况下。本文研究了在更一般的混合域渐近框架下，广义信息准则（GIC）用于选择地质统计回归模型的情况。通过一些统计量的一致收敛发展，我们在某些正则条件下建立了GIC的选择一致性以及渐近损失效率，无论协方差模型是否正确指定。我们进一步提供了满足条件的不同类型解释变量的具体例子。例如，在某些情况下，即使某些空间协方差参数不能一致估计，GIC仍然具有选择一致性。另一方面，在固定域渐近框架下，GIC无法始终一致地选择真实的多项式阶数。此外，显示了区域的增长率以及候选回归器的空间平滑度在模型选择中起着关键作用。 显示英文摘要

摘要： 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.