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Variable Selection in Additive Models by Nonnegative Garrote

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  • Eva Cantoni
  • Joanna Mills Flemming
  • Elvezio Ronchetti

Abstract

We adapt Breiman's (1995) nonnegative garrote method to perform variable selection in nonparametric additive models. The technique avoids methods of testing for which no reliable distributional theory is available. In addition it removes the need for a full search of all possible models, something which is computationally intensive, especially when the number of variables is moderate to high. The method has the advantages of being conceptually simple and computationally fast. It provides accurate predictions and is effective at identifying the variables generating the model. For illustration, we consider both a study of Boston housing prices as well as two simulation settings. In all cases our methods perform as well or better than available alternatives like the Component Selection and Smoothing Operator (COSSO).

Suggested Citation

  • Eva Cantoni & Joanna Mills Flemming & Elvezio Ronchetti, 2006. "Variable Selection in Additive Models by Nonnegative Garrote," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2006.02, Institut d'Economie et Econométrie, Université de Genève.
  • Handle: RePEc:gen:geneem:2006.02
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    References listed on IDEAS

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    1. S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
    2. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
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    Keywords

    cross-validation; nonnegative garrote; nonparametric regression; shrinkage methods; variable selection;

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