Small-sample confidence limits for parameters under inequality constraints with application to quantal bioassay

A family of methods is presented for constructing confidence limits for the parameters of a collection of distributions when a simple ordering is assumed among the parameters. The methods are shown to yield confidence limits that are exact or conservative for finite samples. For discrete distributions, one of the methods produces confidence limits that are at least as tight as the limits produced by a commonly used single-sample procedure. Confidence limits are demonstrated for a binomial quantal bioassay problem assuming a nondecreasing dose-response function. Results of a simulation study show that competing asymptotic methods can produce serious discrepancies between nominal and actual coverage probabilities for binomial samples of sizes up to 30, and demonstrate that the new approach can be competitive with the asymptotic methods when the latter maintain their nominal error rates.