Informative goodness-of-fit for multivariate distributions

Abstract

This article discusses an informative goodness-of-fit (iGOF) approach to study multivariate distributions. When the null model is rejected, iGOF allows us to identify the underlying sources of mismodeling and naturally equips practitioners with additional insights on the nature of the deviations from the true distribution. The informative character of the procedure is achieved by exploiting smooth tests and random field theory to facilitate the analysis of multivariate data. Simulation studies show that iGOF enjoys high power for different types of alternatives. The methods presented here directly address the problem of background mismodeling arising in physics and astronomy. It is in these areas that the motivation of this work is rooted.

A novel approach to detect line emission under high background in high-resolution X-ray spectra

“…A more careful and principled method must be used to evaluate their reality. We, therefore, employ the method proposed in (Algeri 2020(Algeri , 2021 to adequately model background shapes on each of the regions considered. Moreover, since our analysis requires us to test for the presence of one or more lines on each of the above-mentioned regions, adequate corrections for multiple hypotheses testing are also implemented.…”

“…For what concerns the deviance statistic, a post-selection adjusted p-value can be constructed as described in Algeri (2021). Specifically, let…”

“…Here, we present a newly developed statistical approach to evaluate the significance of deviations that may be present in highresolution spectra even in the presence of high background (Algeri 2020(Algeri , 2021. The method works by comparing a postulated model for the background and a source-free background dataset, to assess the validity of the former and, if needed, provide a data-driven correction for it based on the information carried by the latter.…”