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Estimating the structural dimension of regressions via parametric inverse regression. (English) Zbl 0979.62041
Summary: 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.

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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