Abstract
An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne’s test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.
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