In many applications it is known that the underlying smooth function is constrained to have a specific form. In the present paper, we propose an estimation method based on the regression spline approach, which allows to include concavity or convexity constraints in an appealing way. Instead of...

We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in terms of a generous amount of B-Splines basis functions. In...

In recent years the introduction of aggregation methods led to many new techniques within the field of prediction and classification. The most important developments, bagging and boosting, habe been extensively analyzed for two and multi class problems. While the proposed methods treat the class...

A new regularization method for regression models is proposed. The criterion to be minimized contains a penalty term which explicitly links strength of penalization to the correlation between predictors. As the elastic net, the method encourages a grouping effect where strongly correlated...

The use of generalized additive models in statistical data analysis suffers from the restriction to few explanatory variables and the problems of selection of smoothing parameters. Generalized additive model boosting circumvents these problems by means of stagewise fitting of weak learners. A...

Ridge regression is a well established method to shrink regression parameters towards zero, thereby securing existence of estimates. The present paper investigates several approaches to combining ridge regression with boosting techniques. In the direct approach the ridge estimator is used to fit...

Emerging patterns represent a class of interaction structures which has been recently proposed as a tool in data mining. In this paper, a new and more general definition refering to underlying probabilities is proposed. The defined interaction patterns carry information about the relevance of...

In linear mixed models the influence of covariates is restricted to a strictly parametric form. With the rise of semi- and nonparametric regression also the mixed model has been expanded to allow for additive predictors. The common approach uses the representation of additive models as mixed...

A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of...