Estimating the structural dimension of regressions via parametric inverse regression |
| |
Authors: | Efstathia Bura,& R. Dennis Cook |
| |
Affiliation: | George Washington University, Washington DC, USA,;University of Minnesota, St Paul, USA |
| |
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. |
| |
Keywords: | Asymptotic test for dimension Dimension reduction Inverse regression Parametric inverse regression Sliced inverse regression |
|
|