### 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.

Original language | English (US) |
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Pages (from-to) | 393-410 |

Number of pages | 18 |

Journal | Journal of the Royal Statistical Society. Series B: Statistical Methodology |

Volume | 63 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2001 |

### Keywords

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