Estimating the structural dimension of regressions via parametric inverse regression

Efstathia Bura, R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

108 Scopus citations


A new estimation method for the dimension of a regression at the outset of an analysis is proposed. A linear subspace spanned by projections of the regressor vector X, which contains part or all of the modelling information for the regression of a vector Y on X, and its dimension are estimated via the means of parametric inverse regression. Smooth parametric curves are fitted to the p inverse regressions via a multivariate linear model. No restrictions are placed on the distribution of the regressors. The estimate of the dimension of the regression is based on optimal estimation procedures. A simulation study shows the method to be more powerful than sliced inverse regression in some situations.

Original languageEnglish (US)
Pages (from-to)393-410
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - 2001


  • Asymptotic test for dimension
  • Dimension reduction
  • Inverse regression
  • Parametric inverse regression
  • Sliced inverse regression


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