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) |
|---|---|
| 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 - 2001 |
Keywords
- Asymptotic test for dimension
- Dimension reduction
- Inverse regression
- Parametric inverse regression
- Sliced inverse regression