Statistical inference for inverse problems

Nicolai Bissantz and Hajo Holzmann

No 2007,40, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: In this paper 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.

Keywords: Asymptotic normality; confidence interval; deconvolution; heat equation; modality; statistical inference; statistical inverse problem (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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