Nonparametric regression as an example of model choice - Paul Lyndon Davies; Ursula Gather; Henrike Weinert (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2006)
Nonparametric regression can be considered as a problem of model choice. In this paper 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 behaviour 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 L1 norms and the ability to identify peaks.
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