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On a separation theorem for generalized eigenvalues and a problem in the analysis of sample surveys. (English) Zbl 0587.62023
Methods have been developed earlier for analyzing multiway tables of categorical data in complex sample surveys which use log-linear models. In this paper bounds are obtained for the asymptotic percentage points of chi-squared tests of fit for these log-linear models. These bounds are obtained by using certain separation inequalities for the generalized eigenvalues of a matrix X’AX with respect to a matrix X’BX, when both A and B are assumed to be non-negative definite.
Reviewer: T.J.Rao

MSC:
62D05 Sampling theory, sample surveys
62G10 Nonparametric hypothesis testing
15A18 Eigenvalues, singular values, and eigenvectors
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