A boosting approach to generalized monotonic regression

Abstract

We propose a novel approach for generalized additive regression problems, where one or more smooth components are assumed to have monotonic influence on the dependent variable. The response is allowed to follow a simple exponential family. Smooth estimates are obtained by expansion of the unknown functions into B-spline basis functions, where the degree of smoothness is regularized by penalization. Monotonicity of estimates is achieved by restricting estimated coefficients to form an increasing sequence. Estimation is done by applying recently developed componentwise boosting methods for regression purposes. The performance of the new approach is demonstrated on numerical examples.