Component selection and smoothing for nonparametric regression in exponential families

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20 Scopus citations

Abstract

We propose a new penalized likelihood method for model selection and nonparametric regression in exponential families. In the framework of smoothing spline ANOVA, our method employs a regularization with the penalty functional being the sum of the reproducing kernel Hilbert space norms of functional components in the ANOVA decomposition. It generalizes the LASSO in the linear regression to the nonparametric context, and conducts component selection and smoothing simultaneously. Continuous and categorical variables are treated in a unified fashion. We discuss the connection of the method to the traditional smoothing spline penalized likelihood estimation. We show that an equivalent formulation of the method leads naturally to an iterative algorithm. Simulations and examples are used to demonstrate the performances of the method.

Original languageEnglish (US)
Pages (from-to)1021-1041
Number of pages21
JournalStatistica Sinica
Volume16
Issue number3
StatePublished - Jul 1 2006
Externally publishedYes

Keywords

  • Exponential family
  • LASSO
  • Nonparametric regression
  • Penalized likelihood
  • Smoothing spline ANOVA

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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