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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.

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
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