This note constructs a possibilistic IM for marginal inference on two normally distributed means, highlighting efficiency improvements over standard approaches.
The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves only two normally distributed data points with a constraint that the pair of means are not too far apart from one another. Starting with a regularized ML estimator, we construct a novel possibilistic IM for marginal inference on one of the two means. Not only does the new IM remain valid, it is also more efficient than the standard marginal inference ignoring the a priori information about the closeness of means, as well as the partial conditioning IM solution recently proposed in Yang et al. (2023).
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Liu et al. (2025) studied this question.
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