On a separation theorem for generalized eigenvalues and a problem in the analysis of sample surveys

Abstract We obtain usable bounds for the asymptotic percentage points of chi-squared tests of fit for log-linear models fitted to contingency tables estimated from survey data, by applying some new separation inequalities for the generalized eigenvalues of a matrix X′AX with respect to a matrix X′BX , when both the matrices A and B are nonnegative definite. We also present some historical remarks on the Poincare separation theorem for eigenvalues from which our new inequalities are shown to follow.

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