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arXiv · 1702.05545

Some Theorems on Optimality of a Single Observation Confidence Interval for the Mean of a Normal Distribution

Stephen Portnoy
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Abstract

We consider the problem of finding a proper confidence interval for the mean based on a single observation from a normal distribution with both mean and variance unknown. Portnoy (2017) characterizes the scale-sign invariant rules and shows that the Hunt-Stein construction provides a randomized invariant rule that improves on any given randomized rule in the sense that it has greater minimal coverage among all procedures with a fixed expected length. Mathematical results here provide a specific mixture of two non-randomized invariant rules that achieve the minimax optimality. A multivariate confidence set based on a single observation vector is also developed.

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Stephen Portnoy. 2017-02-18. Some Theorems on Optimality of a Single Observation Confidence Interval for the Mean of a Normal Distribution. https://arxiv.org/abs/1702.05545

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