Estimation and Prediction for Geostatistical Regression Models via a Corrected SURE

• Activity Number: 314
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Chun-Shu Chen* and Hong-Ding Yang
• Companies: National Changhua University of Education and National Changhua University of Education
• Keywords: Geostatistics ; Matern covariogram ; Parameter estimation ; Smoothing parameter ; Spatial prediction

Abstract

We consider geostatistical regression models to predict spatial variables of interest and the model parameters are estimated by the likelihood-based methods. It is known that the covariance parameters cannot be estimated well even when increasing amounts of data are collected densely in a fixed domain, and hence the prediction would be inaccurate. Although a best linear unbiased predictor has been used when model parameters are known, a predictor after plugging-in estimated parameters is nonlinear and hence may be not the best in practice. Therefore, we propose an adjusted covariance parameter estimation method via minimizing a corrected Stein's unbiased risk estimator. The resulting adjusted parameter estimators perform better than the conventional likelihood-based estimators, and the spatial predictor is more accurate and stable. The validities of the proposed method are justified both theoretically and numerically.