×

zbMATH — the first resource for mathematics

Determining the dimensionality in sliced inverse regression. (English) Zbl 0791.62069
Summary: A general regression problem is one in which a response variable can be expressed as some function of one or more different linear combinations of a set of explanatory variables as well as a random error term. Sliced inverse regression is a method for determining these linear combinations. We address the problem of determining how many linear combinations are involved. Procedures based on conditional means and conditional covariance matrices, as well as a procedure combining the two approaches, are considered. In each case we develop a test that has an asymptotic chi-squared distribution when the vector of explanatory variables is sampled from an elliptically symmetric distribution.

MSC:
62J02 General nonlinear regression
62J99 Linear inference, regression
62H15 Hypothesis testing in multivariate analysis
62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
PDF BibTeX XML Cite
Full Text: DOI