The principle of minimum discrimination information estimation is employed to obtain RBAN (Regular Best Asymtotically Normal) estimates of the cell frequencies of anr×rcontingency table under hypotheses of either symmetry or marginal homogeneity. For the latter, a convergent iterative procedure is given to compute the estimates. The associated minimum discrimination information statistics are distributed asymptotically as χ2under the null hypotheses. The procedures differ from those previously presented in the literature and permit of extension to multidimensional contingency tables. An example is given.