Parametric versus non - parametric modelling ? Statistical evidence based on P - value curves

In astrophysical (inverse) regression problems it is an important task to decide whether a given parametric model describes the observational data sufficiently well or whether a non-parametric modelling becomes necessary. However, in contrast to common practice this cannot be decided by solely comparing the quality of fit due to possible over-fitting by the non-parametric method. Therefore, in this paper we present a resampling algorithm which allows to decide whether deviations between a parametric and a non-parametric model are systematic or due to noise. The algorithm is based on a statistical comparison of the corresponding residuals, under the assumption of the parametric model as well as under violation of this assumption. This yields a graphical tool for a robust decision making of parametric versus non-parametric modelling. Moreover, our approach can be used for the selection of the most proper model among several competitors (model selection). The methods are illustrated by the problem of recovering the luminosity density in the Milky Way [MW] from near-infrared [NIR] surface brightness data of the DIRBE experiment on board of the COBE satellite. Among the parametric models investigated one with 4-armed spiral structure performs best. In this model the Sagittarius-Carina arm and its counter-arm are significantly weaker than the other pair of arms. Furthermore, we find statistical evidence for an improvement over a range of parametric models with different spiral structure morphologies by a non-parametric model of Bissantz & Gerhard (2002).