In classical smoothing splines, the smoothness is controlled by a single smoothing parameter that penalizes the roughness uniformly across the whole domain. Adaptive smoothing splines extend this framework to allow the smoothing parameter to change in the domain, adapting to the change of roughness. In this article we propose a data driven method to nonparametrically model the penalty function....

A computational scheme for fitting smoothing spline ANOVA models to large data sets with a (near) tensor product design is proposed. Such data sets are common in spatial-temporal analyses. The proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time. Several ways to further speed up the backfitting algorithm, such a...

Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivity are explained, including the breakdown of several popular data-driven smoothing parameter selection methods. We review the existing literature in kernel regression, smoothing splines and wavelet regression under correlation, both for short-range an...

Objectives. This article examines the timing of change in criminal offending relative to entrance into parenthood, in light of four competing theoretical frameworks (social control, routine activities, strain and cognitive transformation). Moreover, it analyzes whether criminal trends are gender or country specific. Methods. Using samples of high-risk men and women in The Netherlands and Norway...

In this paper, we propose and validate a computationally efficient non-iterative domain decomposition procedure for calculating bivariate cubic L1 smoothing splines. This domain decomposition procedure involves calculating local L1 smoothing splines individually on overlapping “extended subdomains” that cover the global domain and then creating the global L1 smoothing spline by patching togethe...

In this paper we introduce a characterization of the log density smoothing spline ANOVA model. We show that in a log density ANOVA model of order r (consisting of the main effects and all the interactions of order up to r), the joint density function is uniquely determined by the collection of all r dimensional marginal densities. Furthermore, the order r model is the largest log density ANOVA ...

Accurate and plausible 3D face reconstruction remains a difficult problem up to this day, despite the tremendous advances in computer technology and the continuous growth of the applications utilizing 3D face models (e.g. biometrics, movies, gaming). In this paper, a two-step technique for efficient 3D face reconstruction from a set of face images acquired using an uncalibrated camera is presen...

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalized spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. Further, they allow straightforward extensions to multiple auxiliary variables and to complex designs. Unde...

We adapt the interactive spline model of Wahba to growth curves with covariates. The smoothing spline formulation permits a nonparametric representation of the growth curves. In the limit when the discretization error is small relative to the estimation error, the resulting growth curve estimates often depend only weakly on the number and locations of the knots. The smoothness parameter is dete...

This document reproduces the data analyses presented in Bühlmann and Hothorn (2007). For a description of the theory behind applications shown here we refer to the original manuscript. The results differ slightly due to technical changes or bugfixes in mboost that have been implemented after the paper was printed. Most important, gamboost uses penalized B-splines instead of smoothing splines as...