Estimation of proportions for multinomial contingency tables subject to marginal constraints

For a two-way table of observed proportions we consider four approaches to the problem of fitting a new set of proportions which-subject to satisfying marginal constraints on row and column totals-corresponds as closely as possible to the original table, The approaches are known to be asymptotically equivalent; but our chief interest is in establishing, at least for the 2x2 table, a hierarchy of preferences under multinomial sampling for moderate sample sizes. Implementation of minimum chi-square is described and recommended.