Transforming Contingency Tables

Abstract : We present a general theorem on transforming contingency tables and several applications where the transformation technique has allowed us to take advantage of the Iterative Proportional Fitting Procedure and has resulted in simple and useful procedures. A further advantage of this technique is that it is sometimes possible to recognize closed-form estimates in the transformed problem while they would be overlooked in the original setting. We shall view the estimation problem as one of minimizing the Kullback-Leibler information distance between two probability mass functions and will roughly follow the notation of Csiszar (1976). Although we have adopted the information distance point of veiw, the duality between maximum likelihood estimation and minimum information estimation (see e.g. Darroch and Ratcliff (1972)) implies that the results of this paper can just as well be interpreted from the maximum likelihood point of view.