Spatial Prediction Variance Estimation based on Generalized Degrees of Freedom

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Roberto Rivera*+
• Companies: University of Puerto Rico at Mayaguez
• Keywords: Spatial prediction variance estimation ; Generalized degrees of freedom ; mean squared prediction error ; EBLUP variance ; bootstrapping

Abstract

In practice rarely (if ever) is the spatial covariance known in spatial prediction problems. Often, prediction is performed after estimated spatial covariance parameters are plugged into the prediction equation. The estimated spatial association parameters are also plugged into the prediction variance of the spatial predictor. However, simply plugging in spatial covariance parameter estimates into the prediction variance of the spatial predictor does not take into account the uncertainty in the true values of the spatial covariance parameters. Therefore the plug-in prediction variance estimate will underestimate the true prediction variance of the estimated spatial predictor, especially for small datasets. We propose a new way to estimate the prediction variance of the estimated spatial predictor based on Generalized Degrees of Freedom using parametric bootstrapping. Our new estimator is is compared to three other prediction variance estimators proposed in literature. The new prediction variance estimator sometimes performs best among the four prediction variance estimators compared.