Minimum-area confidence sets for a normal distribution |
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Authors: | Jesse Frey Osvaldo MarreroDouglas Norton |
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Institution: | Department of Mathematical Sciences, Villanova University, Villanova, PA 19085, USA |
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Abstract: | 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. |
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Keywords: | Confidence band Cumulative distribution function Joint confidence region |
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