SPLINE SMOOTHING WITH MODEL-BASED PENALTIES

Nonparametric regression techniques, which estimate functions directly from noisy data rather than relying on specific parametric models, no w play a central role in statistical analysis. We can improve the effi ciency and other aspects of a nonparametric curve estimate by using pr ior knowledge about general features of the curve in the smoothing pro cess. Spline smoothing is extended in this paper to express this prior knowledge in the form of a linear differential operator that annihila tes a specified parametric model for the data. Roughness in the fitted function is defined in terms of the integrated square of this operato r applied to the fitted function. A fast O(n) algorithm is outlined fo r this smart smoothing process. Illustrations are provided of where th is technique proves useful.