Nonparametric Regression as an Example of Model Choice

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.

Keywords:

• Nonparametric regression
• Model choice
• Approximation

Mathematics Subject Classification:

• 62G08
• 62G05

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).