Nonparametric Additive Modeling by Smoothing Splines: Robust Unbiased-Risk-Estimate Selector and a Nonisotropic-Smoothing Improvement

http://demonstrations.wolfram.com/NonparametricAdditiveModelingBySmoothingSplinesRobustUnbiase/.Nonparametric Additive Modeling by Smoothing Splines: Robust Unbiased-Risk-Estimate Selector and a Nonisotropic-Smoothing Improvementhttp://demonstrations.wolfram.com/NonparametricAdditiveModelingBySmoothingSplinesRobustUnbiase/.Nonparametric Additive Modeling by Smoothing Splines: Robust Unbiased-Risk-Estimate Selector and a Nonisotropic-Smoothing Improvement.An earlier series of Demonstrations of the Wolfram Demonstrations Project concerned the well-known cross-validation approach to optimally estimate smooth univariate regression functions. Notably, the demonstration "Nonparametric Regression and Kernel Smoothing: Confidence Regions for the L2-Optimal Curve Estimate," analyzes, on simple examples, how one can construct good confidence statements (asymptotically justified) about the optimal amount of smoothing, and the demonstration "Nonparametric Curve Estimation by Smoothing Splines: Unbiased-Risk-Estimate Selector and Its Robust Version via Randomized Choices" illustrates that the selector (a variant of cross-validation) can be easily robustified via randomized choices. The present Demonstration discusses an extension of the latter robustification method to a simple bivariate context. Specifically, we model and compute using the well-known backfitting algorithm, by additive cubic smoothing splines. Furthermore, this Demonstration introduces a natural nonisotropy in the smoothing operators