Abstract
Nonparametric regression can be considered as a problem of model choice. In this article, we present the results of a simulation study in which several nonparametric regression techniques including wavelets and kernel methods are compared with respect to their behavior on different test beds. We also include the taut-string method whose aim is not to minimize the distance of an estimator to some “true” generating function f but to provide a simple adequate approximation to the data. Test beds are situations where a “true” generating f exists and in this situation it is possible to compare the estimates of f with f itself. The measures of performance we use are the L2- and the L∞-norms and the ability to identify peaks.
Acknowledgment
This work has been supported by the Collaborative Research Center ‘Reduction of Complexity in Multivariate Data Structures’ (SFB 475) of the German Research Foundation (DFG).