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Estimating the structural dimension of regressions via parametric inverse regression

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  • Efstathia Bura
  • R. Dennis Cook

Abstract

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.

Suggested Citation

  • Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:2:p:393-410
    DOI: 10.1111/1467-9868.00292
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