Optimal model averaging by data perturbation for spatial noisy data

Abstract

Geostatistical models play an important role in spatial data analysis, in which model selection is inevitable. Model selection methods, such as AIC and BIC, are popular for selecting appropriate models. In recent years, some model averaging methods, such as smoothed AIC and smoothed BIC, are also applied to spatial data models. However, the corresponding averaging estimators are outperformed by optimal model averaging estimators (Hansen in Econometrica 75:1175–1189, 2007) for the ordinary linear models. Therefore, this paper focuses on the optimal model averaging method for geostatistical models. We propose a weight choice criterion for the model averaging estimator on the basis of the generalized degrees of freedom and data perturbation technique. We further theoretically prove the resultant estimator is asymptotically optimal in terms of the mean squared error, and numerically demonstrate its satisfactory performance. Finally, the proposed method is applied to a mercury data set.