New Statistical Goodness of Fit Techniques Applied to the Recovery of the Milky Way Near-IR Luminosity Density Distribution - the 'Wild Bootstrap' Approach

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. Then, for example, a least squares fit results in a parameter estimate. In a second step various kinds of χ2 goodness of fit measures are applied to assess whether the deviation between data and the model with the estimated parameters is due to random noise and not to systematic departures from the model. We present a new method which is applicable in noisy versions of Fredholm integral equations of the first kind. For the second step we suggest a bootstrap algorithm which allows an approximation of the distribution of the suggested test statistic.