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Variable Selection in Additive Models Using P-Splines

Summary: This article extends the nonnegative garrote method to a component selection method in a nonparametric additive model in which each univariate function is estimated with P-splines. The authors also establish the consistency of the procedure. An advantage of P-splines is that the fitted function is represented in a rather small basis of B-splines. A numerical study illustrates the finite-sample performance of the method and includes a comparison with other methods. The nonnegative garrote method with P-splines has the advantage of being computationally fast. Additionally, With the implementation of an appropriate parameter selection procedure, the method performs very well. Real data analysis leads to interesting findings. Supplementary materials for this article (technical proofs, additional numerical results, R code) are available online.

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  • Topics: Design of Experiments
  • Keywords: Nonparametric methods, Data smoothing, Spline functions, Variable selection, Regression analysis
  • Author: Antoniadis, Anestis; Gijbels, Irène; Verhasselt, Anneleen;
  • Journal: Technometrics