Bissantz, Nicolai; Holzmann, Hajo Statistical inference for inverse problems. (English) Zbl 1137.62325 Inverse Probl. 24, No. 3, Article ID 034009, 17 p. (2008). Summary: We study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima of the unknown function. The methods are illustrated in a case study, where we analyze the distribution of heliocentric escape velocities of galaxies in the Centaurus galaxy cluster, and provide statistical evidence for its bimodality. Cited in 24 Documents MSC: 62G07 Density estimation 62G15 Nonparametric tolerance and confidence regions 62G08 Nonparametric regression and quantile regression 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 85A35 Statistical astronomy PDFBibTeX XMLCite \textit{N. Bissantz} and \textit{H. Holzmann}, Inverse Probl. 24, No. 3, Article ID 034009, 17 p. (2008; Zbl 1137.62325) Full Text: DOI Link