Chi-squared tests are considered for testing homogeneity against an order restriction and for testing an order restriction against all alternatives on multinomial parameters. Closed-form expressions are obtained for the minimum chi-squared estimator and the Neyman modified chisquared estimator. The asymptotic equivalence between these chi-squared tests and the likelihood ratio test is established. The latter has been studied by Robertson (1978). Their asymptotic null distribution is the chi-bar-squared distri…
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