Smoothing with Curvature Constraints based on Boosting Techniques

Leitenstorfer, Florian and Tutz, Gerhard (2006): Smoothing with Curvature Constraints based on Boosting Techniques. Collaborative Research Center 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.

• Item Type: Paper (Research Paper)
• Keywords: Shape constrained smoothing, Concavity, Regression splines, Boosting
• Collections: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics
• Language: English