an:00579821
Zbl 0791.62069
Schott, James R.
Determining the dimensionality in sliced inverse regression
EN
J. Am. Stat. Assoc. 89, No. 425, 141-148 (1994).
00018512
1994
j
62J02 62J99 62H15 62J05 62F03 62E20
eigenprojection; projection matrix; linear combinations of explanatory variables; sliced inverse regression; general regression problem; response variable; conditional means; conditional covariance matrices; asymptotic chi-squared distribution; elliptically symmetric distribution
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.