A Locally Adaptive Penalty for Estimation of Functions With Varying Roughness

We propose a new regularization method called Loco-Spline for nonparametric function estimation. Loco-Spline uses a penalty which is data driven and locally adaptive. This allows for more flexible estimation of the function in regions of the domain where it has more curvature, without over fitting in regions that have little curvature. This methodology is also transferred into higher dimensions via the Smoothing Spline ANOVA framework. General...