Smoothing with Curvature Constraints based on Boosting Techniques

Leitenstorfer, Florian und Tutz, Gerhard (2006): Smoothing with Curvature Constraints based on Boosting Techniques. Sonderforschungsbereich 386, Discussion Paper 467

Abstract

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 using linear or quadratic programming routines, we handle the required inequality constraints on basis coefficients by boosting techniques. Therefore, recently developed componentwise boosting methods for regression purposes are applied, which allow to control the restrictions in each iteration. The proposed approach is compared to several competitors in a simulation study. We also consider a real world data set.

• Dokumententyp: Paper
• Keywords: Shape constrained smoothing, Concavity, Regression splines, Boosting
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch