New Statistical Goodness-of-Fit Techniques in Noisy Inhomogeneous Regression Problems with an Application to the Problem of Recovering of the Luminosity Density of the Milky Way from Surface Brightness Data

Abstract

Fitting models to regression data is an important part of astronomers everyday work. A common proceeding is based on the assumption, that a parametric class of functions describes the data structure sufficiently well. We present a new method which is applicable in noisy versions of Fredholm integral equations of the first kind, and an associated goodness of fit measure, which works under the assumption that the parametric model in question holds for the data. For this we suggest a bootstrap algorithm which allows an approximation of the distribution of the suggested test statistic. Then we switch to the assumption that the model under consideration does not hold, and present a method to compare parametric models under this assumption. This second method is based on the same bootstrap algorithm as the first method. As an example we finally apply our methods to the problem of recovering the luminosity density of the Milky Way from data of the DIRBE experiment on board of the COBE satellite. We present statistical evidence for flaring of the stellar disk inside the solar circle.