Estimating the structural dimension of regressions via parametric inverse regression

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 re gressor vector X, which contains part or all of the modelling information f or the regression of a vector Y on X, and its dimension are estimated via t he means of parametric inverse regression. Smooth parametric curves are fit ted to the p inverse regressions via a multivariate linear model. No restri ctions are placed on the distribution of the regressors. The estimate of th e dimension of the regression is based on optimal estimation procedures. A simulation study shows the method to be more powerful than sliced inverse r egression in some situations.