ESTIMATING EXACT P-VALUES BY THE METHOD OF CONTROL VARIATES OR MONTE-CARLO RESCUE

Despite algorithmic advances in exact nonparametric inference, problem s often occur that are too large for exact p value computations but to o sparse for reliable asymptotic results. In these situations Monte Ca rlo methods are a good compromise. They bound the true p value within a confidence interval. But a factor discouraging the use of Monte Carl o p values is their sensitivity to the random number sequence. One can overcome this drawback by computing a 99% C.I, confidence interval of width less than .0001. Then the estimated p values become insensitive to the random number sequence up to three decimals. For all practical purposes, these estimates are invariant to random number sequences. T he usual Monte Carlo method requires millions of samples to yield such an invariant estimate. The Monte Carlo scheme presented here decrease s the sample size by two to three orders of magnitude. We illustrate t his method with tests for r x c tables, two-sample survival data, and stratified 2 x 2 tables.