MARS: Selecting basis functions and knots with an empirical Bayes method

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3 Citations (Scopus)

Abstract

An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed, which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that is relatively parsimonious and more stable for some example data sets.

Original languageEnglish
Pages (from-to)583-597
Number of pages15
JournalComputational Statistics
Volume22
Issue number4
DOIs
Publication statusPublished - Dec 1 2007
Externally publishedYes

Keywords

  • Akaike Bayes information criterion
  • Estimation of interaction terms
  • Marginal likelihood
  • Multivariate adaptive regression
  • Penalized likelihood approach

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics

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