Abstract
In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these populations are in simple tree order. We provide an asymptotic representation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be \( \sqrt n \)-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.
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