Confidence intervals in general regression models that utilize uncertain prior information

Abstract

– We consider a general regression model, either without a scale parameter or with a known scale parameter. We construct a confidence interval for a scalar parameter of interest that utilizes the uncertain prior information that a distinct scalar parameter takes a specified value. This confidence interval has excellent coverage properties. It also has local scaled expected length, where the scaling is with respect to the usual confidence interval, that (a) is substantially less than 1 when the prior information is correct, (b) has a maximum value that is not too large, and (c) is close to 1 when the data and prior information are highly discordant. An important practical application of this confidence interval is to a quantal bioassay carried out to compare two similar compounds. In this context, the uncertain prior information is that the hypothesis of “parallelism” holds. We provide extensive numerical results that illustrate the attractive properties of this confidence interval in this context.