SEQUENTIAL MONTE CARLO METHODS FOR PERMUTATION TESTS ON TRUNCATED DATA

The permutation test is one of the oldest techniques for making statis- tical inferences. Monte Carlo methods and asymptotic formulas have been used to approximate the associated p-values. When data are truncated, however, the permutation null distribution is difficult to handle. We describe here an efficient se- quential importance sampling strategy for generating permutations with restricted positions, which provides accurate p-value approximations in all examples we have tested. The algorithm also provides good estimates of permanents of zero-one matri- ces, which by itself is a challenging problem. The key to our strategy is a connection between allowable permutations and zero-one tables with structural zeros.

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