We describe a sequential importance sampling approach to making conditional inferences on two-way zero-one and contingency tables with fixed marginal sums and a given set of structural zeros. Our method enables us to approximate closely the null distributions of various test statistics about these tables, as well as to obtain an accurate estimate of the total number of tables satisfying the constraints. Our method compares favorably with other existing Monte Carlo algorithms, and is sometimes a few orders of magnitude more efficient.

KEY WORDS: Contingency table, Exact test, Monte Carlo method, Sequential importance sampling, Structural zero, Zero-one table.

Please email Yuguo Chen (yuguo@stat.duke.edu) for a copy of the paper.