Smoothing Parameter Selection Methods for Nonparametric Regression with Spatially Correlated Errors

Nonparametric regression makes it possible to visualize and describe spatial trends without requiring the specification of a parametric model, but appropriate choice of smoothing parameters is important to avoid misinterpreting the nonparametric fits. Because spatial data are often correlated, currently available data-driven smoothing parameter selection methods often fail to provide useful results. We propose to adjust the generalized cross-validation (GCV) criterion for the effect of the spatial correlation, and develop an approach to do so in the case of bivariate local polynomial regression. The adjustment uses a pilot fit to the data and the estimation of a parametric covariance model. The method is easy to implement, and we show that it leads to improved smoothing parameter selection results, even when the covariance ∗email: [email protected]