Surface estimation, variable selection, and the nonparametric oracle property

Curtis B. Storlie, Howard D. Bondell, Brian J. Reich, Hao Helen Zhang

Research output: Contribution to journalArticle

59 Scopus citations

Abstract

Variable selection for multivariate nonparametric regression is an important, yet challenging, problem due, in part, to the infinite dimensionality of the function space. An ideal selection procedure would be automatic, stable, easy to use, and have desirable asymptotic properties. In particular, we define a selection procedure to be nonparametric oracle (np-oracle) if it consistently selects the correct subset of predictors and, at the same time, estimates the smooth surface at the optimal nonparametric rate, as the sample size goes to infinity. In this paper, we propose a model selection procedure for nonparametric models, and explore the conditions under which the new method enjoys the aforementioned properties. Developed in the framework of smoothing spline ANOVA, our estimator is obtained via solving a regularization problem with a novel adaptive penalty on the sum of functional component norms. Theoretical properties of the new estimator are established. Additionally, numerous simulations and examples suggest that the new approach substantially outperforms other existing methods in the finite sample setting.

Original languageEnglish (US)
Pages (from-to)679-705
Number of pages27
JournalStatistica Sinica
Volume21
Issue number2
DOIs
StatePublished - Apr 2011
Externally publishedYes

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Keywords

  • Adaptive LASSO
  • Nonparametric regression
  • Regularization method
  • Smoothing spline ANOVA
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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