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Efficiency of the V -Fold Model Selection for Localized Bases

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Nonparametric Statistics (ISNPS 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 250))

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Abstract

Many interesting functional bases, such as piecewise polynomials or wavelets, are examples of localized bases. We investigate the optimality of V -fold cross-validation and a variant called V -fold penalization in the context of the selection of linear models generated by localized bases in a heteroscedastic framework. It appears that while V -fold cross-validation is not asymptotically optimal when V is fixed, the V -fold penalization procedure is optimal. Simulation studies are also presented.

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Author information

Authors and Affiliations

  1. CREST-ENSAI-UBL, Bruz, France

    F. Navarro & A. Saumard

Authors
  1. F. Navarro
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  2. A. Saumard
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Corresponding author

Correspondence to F. Navarro .

Editor information

Editors and Affiliations

  1. MODAL’X, Paris West University Nanterre La Défense, Nanterre, France

    Patrice Bertail

  2. LMA, Avignon University, Avignon, France

    Delphine Blanke

  3. MIASHS, University of Rennes 2, Rennes, France

    Pierre-André Cornillon

  4. Formation Continue CEPE, Ecole Nationale de la Statistique et de l’Administration, Malakoff, France

    Eric Matzner-Løber

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Navarro, F., Saumard, A. (2018). Efficiency of the V -Fold Model Selection for Localized Bases. In: Bertail, P., Blanke, D., Cornillon, PA., Matzner-Løber, E. (eds) Nonparametric Statistics. ISNPS 2016. Springer Proceedings in Mathematics & Statistics, vol 250. Springer, Cham. https://doi.org/10.1007/978-3-319-96941-1_4

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