Minimum-area confidence sets for a normal distribution

When making inference on a normal distribution, one often seeks either a joint confidence region for the two parameters or a confidence band for the cumulative distribution function. A number of methods for constructing such confidence sets are available, but none of these methods guarantees a minimum-area confidence set. In this paper, we derive both a minimum-area joint confidence region for the two parameters and a minimum-area confidence band for the cumulative distribution function. The minimum-area joint confidence region is asymptotically equivalent to other confidence regions in the literature, but the minimum-area confidence band improves on existing confidence bands even asymptotically.