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The Empirical Process of Residuals from an Inverse Regression

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Abstract

In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated using a series estimator motivated by a spectral cutoff technique. Further, we investigate the empirical process of residuals from this regression, and show that it satisfies a functional central limit theorem.

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Acknowledgments

This work has been supported in part by the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823, Project C1) of the German Research Foundation (DFG) and the Bundesministerium für Bildung und Forschung through the project “MED4D: Dynamic medical imaging: Modeling and analysis of medical data for improved diagnosis, supervision and drug development”.

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  1. Ruhr-Universität Bochum, Bochum, Germany

    T. Kutta, N. Bissantz, J. Chown & H. Dette

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  1. T. Kutta
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  2. N. Bissantz
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  4. H. Dette
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Correspondence to T. Kutta, N. Bissantz, J. Chown or H. Dette.

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Kutta, T., Bissantz, N., Chown, J. et al. The Empirical Process of Residuals from an Inverse Regression. Math. Meth. Stat. 28, 104–126 (2019). https://doi.org/10.3103/S1066530719020029

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