Statistica Sinica 13(2003), 143-162
USING LINEAR SMOOTHERS TO ASSESS THE
STRUCTURAL DIMENSION OF REGRESSIONS
E. Bura
The George Washington University
Abstract:
Sliced Inverse Regression (Li (1991)) is a simple nonparametric estimation
method for the structural dimension of a regression, that is, for the
dimension of the linear subspace spanned by projections of the multidimensional
regressor vector 
that contains part or all of the modelling information
about the regression of a random variable 
on . In this paper, the
nonparametric estimation method is extended to include the family of linear
smoothers. No restrictions are placed on the distribution of the regressors
except for the linearity condition and existence of second moments. An
asymptotic chi-square test for dimension is obtained. Theoretical results are
illustrated with a small comparative simulation study.
Key words and phrases:
Asymptotic chi-square test, dimension reduction, inverse regression.