New statistical goodness of fit techniques in noisy inhomogeneous inverse problems - With application to the recovering of the luminosity distribution of the Milky Way

摘要

The assumption that a parametric class of functions fits the data structuresufficiently well is common in fitting curves and surfaces to regression data.One then derives a parameter estimate resulting from a least squares fit, say,and in a second step various kinds of chi^2 goodness of fit measures, to assesswhether the deviation between data and estimated surface is due to random noiseand not to systematic departures from the model. In this paper we show thatcommonly-used chi^2-measures are invalid in regression models, particularlywhen inhomogeneous noise is present. Instead we present a bootstrap algorithmwhich is applicable in problems described by noisy versions of Fredholmintegral equations. of the first kind. We apply the suggested method to theproblem of recovering the luminosity density in the Milky Way from data of theDIRBE experiment on board the COBE satellite.