Abstract #300350

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JSM 2003 Abstract #300350
Activity Number: 319
Type: Topic Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #300350
Title: Smoothing Parameter Selection Methods for Nonparametric Regression with Spatially Correlated Errors
Author(s): Mario Francisco-Fernandez*+ and Jean D. Opsomer
Companies: University of La Coruña and Iowa State University
Address: Facultad De Informatica, La Coruña, 15071, Spain
Keywords: nonparametric regression ; Generalizad Cross-Validation (GCV) ; semivariogram estimation
Abstract:

We consider the regression model where the predictors are D-variate random variables and the errors are spatially correlated. In a situation like this, traditional data-driven bandwidth selection methods for nonparametric regression fail to provide good bandwidth values. We present a new and practical method for choosing the smoothing parameter for the local linear estimator of the regression function in the presence of spatially correlated errors. The technique is based on correcting the classical Generalized Cross-Validation criterion by including the estimated covariances of the errors in the method. Assuming a parametric shape for the correlation function of the errors, a theoretical justification of the good performance of this method is shown. A by-product of our work is a proof of the consistency of the empirical semivariogram. Finally, a simulation study and an analysis with real data illustrate the selection method proposed.

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