Shape Constraints

Workgroup "Shape constraints"

Head of workgroup: Dr. Pramita Bagchi


  • Prof. Dr. Holger Dette


Compared with parametric regression methods nonparametric methods have the advantage that they avoid misspecification if the class of regression functions is not (exactly) known. In many situations the regression function is completely unknown but there exists some information about its shape. Such information is called "shape constraint" and often comes from an economic, physical or biological context. Examples for shape constraints are monotonicity, convexity or concavity which naturally occur with consumption functions, call price and volatility functions, dose response or growth curves. But also other shape constraints like certain kinds of symmetry occur in some situations. Although the common nonparametric methods result in good estimators with well studied properties, they do not incorporate the required shape constraints. Therefore, it is important to develop nonparametric estimators that incorporate shape constraints. Such estimators can then be used to interprete the data or to construct statistical tests which can be used to check wether such a shape constraint is reasonable from the observed data.