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Statistica Sinica 25 (2015), 135-149

VARIANCE ESTIMATION AND KRIGING PREDICTION
FOR A CLASS OF NON-STATIONARY SPATIAL MODELS
Shu Yang and Zhengyuan Zhu
Iowa State University

Abstract: This paper discusses the estimation and plug-in kriging prediction of a non-stationary spatial process assuming a smoothly varying variance function with an additive independent measurement error. A difference-based kernel smoothing estimator of the variance function and a modified likelihood estimator of the measurement error variance are used for parameter estimation. Asymptotic properties of these estimators and the plug-in kriging predictor are established. A simulation study is presented to test our estimation-prediction procedure. Our kriging predictor is shown to perform better than the spatial adaptive local polynomial regression estimator proposed by Fan and Gijbels (1995) when the measurement error is small.

Key words and phrases: Bandwidth selection, heteroscedasticity, K-fold cross-validation, local polynomial regression, rates of convergence, variance function.

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