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A Relaxed Iterative Projection Algorithm for Rank-Deficient Regression Problems

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The Art of Semiparametrics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Summary

A relaxed iterative projection (abb. RIP) algorithm for arbitrary linear equation systems is described. It has favorable properties with respect to many statistical applications. A major advantage is that convergence can be established without restrictions on the system matrix. Hence certain characteristics of the system matrix such as diagonal dominance are not required. As a result RIP fitting can be applied where backfitting tends to fail, e.g. when regression predictors are substantially correlated (problem of multicollinearity respectively concurvity). Convergence under a suitable choice of the relaxation parameter is derived for general n × m system matrices. The RIP solution of typical equation systems is studied with respect to the correct (analytical) solution. Empirical findings for the practical selection of the relaxation parameter are reported.

The financial support of the FWF Austrian Science Fund in the research project “Konvergenz und Numerik des Backfitting-Algorithmus” is greatly acknowledged.

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Author information

Authors and Affiliations

  1. Institute for Medical Informatics, Statistics and Documentation, Medical University of Graz, A-8036, Graz, Austria

    Michael G. Schimek

  2. Department of Mathematics, Alpen-Adria-University Klagenfurt, A-9020, Klagenfurt, Austria

    Haro Stettner

Authors
  1. Michael G. Schimek
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  2. Haro Stettner
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Editor information

Editors and Affiliations

  1. Institut für Statistik und Ökonometrie, Georg-August-Universität Göttingen, Platz der Göttinger Sieben 5, 37073, Göttingen, Germany

    Stefan Sperlich

  2. Institut für Statistik und Ökonometrie, CASE — Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178, Berlin, Germany

    Wolfgang Härdle

  3. Hudson Advisors Germany GmbH, Hamburger Allee 14, 60486, Frankfurt a. M., Germany

    Gökhan Aydınlı

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© 2006 Physica-Verlag Heidelberg

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Schimek, M.G., Stettner, H. (2006). A Relaxed Iterative Projection Algorithm for Rank-Deficient Regression Problems. In: Sperlich, S., Härdle, W., Aydınlı, G. (eds) The Art of Semiparametrics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/3-7908-1701-5_6

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