A Stabilized and Versatile Spatial Prediction Method

• Activity Number: 254
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Chun-Shu Chen*+
• Companies: National Changhua University of Education
• Keywords: Data perturbation ; Mean squared prediction error ; Model averaging ; Model selection ; Unbiased risk estimate ; Infill asymptotics

Abstract

In spatial statistics, many methods have been proposed for predicting spatial variables of interest, but the covariance parameters involved in the model have been proven difficult to estimate consistently under infill asymptotics. It would result in less accurate estimation and prediction. In this paper, we propose a data perturbation procedure to obtain a stabilized spatial predictor that is not only continuous but also differentiable with respect to the data even after plugging-in the estimated model parameters. In addition, the resulting stabilized spatial predictors obtained from different models may perform differently under different circumstances, leading to investigators need to confront a model selection process. To avoid suffering uncertainty inherent in a model selection procedure, we also propose a weight selection procedure based on an unbiased risk estimate for averaging over a sequence of candidate stabilized spatial predictors, resulting in a versatile spatial predictor that is adaptive with respect to the underlying spatial process. The validity of the proposed spatial prediction method will be justified both numerically and theoretically.