Joint Confidence Sets for the Mean and Variance of a Normal Distribution

Abstract The standard example of an exact joint confidence set provided in elementary textbooks involves normal data., In addition textbooks provide a variety of asymptotic approximate joint confidence sets for (μ, σ2) in such a setting. What is lacking, and what is provided in this article, is a comparative study of the size and actual performance of these confidence sets. A mild surprise arises in the comparison. If the sample size is 100 or more, the asymptotic confidence regions, in addition to being more robust to violations of distributional assumptions, actually outperform the exact region in terms of expected area of the regions.