A note on cuts for contingency tables

In this note, we propose a general method to find cuts for a contingency table. Useful cuts are, in many cases, statistics S-sufficient for the nuisance parameter and S-ancillary for the parameter of interest. In general, cuts facilitate a strong form of parameter separation known to be useful for conditional inference [E.L. Lehmann, Testing Statistical Hypotheses, 2nd ed., Springer, New York, 1997, pp. 546–548]. Cuts also achieve significant dimension reduction, hence, increase computational efficiency. This is particularly true for the inference about cross-tabulated data, usually with a large number of parameters. Depending on the parameter of interest, we propose a flexible transformation to reparameterize the discrete multivariate response distribution. Inference on cell probabilities or odds ratios will require different parameterizations. The reparameterized distribution is not sum-symmetric. Thus, the finding in this paper expands the results in Barndorff-Nielsen [O.E. Barndorff-Nielsen, Information and Exponential Families in Statistical Theory, John Wiley, New York, 1978, pp. 202–206].