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A note on the geometry of the multiresolution criterion

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  • Mildenberger, Thoralf

Abstract

Several recent developments in nonparametric regression are based on the concept of data approximation: They aim at finding the simplest model that is an adequate approximation to the data. Approximations are regarded as adequate iff the residuals ?look like noise?. This is usually checked with the so-called multiresolution criterion. We show that this criterion is related to a special norm (the ?multiresolution norm?), and point out some important differences between this norm and the p-norms often used to measure the size of residuals. We also treat an important approximation problem with regard to this norm that can be solved using linear programming. Finally, we give sharp upper and lower bounds for the multiresolution norm in terms of p-norms.

Suggested Citation

  • Mildenberger, Thoralf, 2006. "A note on the geometry of the multiresolution criterion," Technical Reports 2006,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200636
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    1. Davies, P. L., 2003. "Approximating data and statistical procedures. I. Approximating data," Technical Reports 2003,07, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Davies, P. Laurie, 2002. "Statistical procedures and robust statistics," Technical Reports 2002,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Davies, P. Laurie & Kovac, Arne & Meise, Monika, 2007. "Confidence sets and non-parametric regression," Technical Reports 2007,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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