The Choice of Statistic on Which to Base Tight Upper Confidence Limits

We consider the problem of finding an upper 1 –α confidence limit (α < ½) for a scalar parameter of interest θ in the presence of a nuisance parameter vector ψ when the data are discrete. Using a statistic T as a starting point, Kabaila & Lloyd (1997) define what they call the tight upper limit with respect to T . This tight upper limit possesses certain attractive properties. However, these properties provide very little guidance on the choice of T itself. The practical recommendation made by Kabaila & Lloyd (1997) is that T be an approximate upper 1 –α confidence limit for θ rather than, say, an approximately median unbiased estimator of θ. We derive a large sample approximation which provides strong theoretical support for this recommendation.