Abstract For one-parameter exponential families, we provide a unified minimax result for estimating the mean under weighted squared error losses in presence of a lower-bound restriction. The finding recovers cases for which the result is known, as well as others which are new such as for a negative binomial model. We also study a related self-minimaxity property, obtaining several non-minimax results. Finally, for discrete models such as Poisson and negative binomial, we obtain classes of minimax estimators of a lower-bound restriction on the mean, which include range preserving solutions.

中文翻译：

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单参数指数族受限均值的极小极大估计

摘要 对于单参数指数族，我们提供了一个统一的极小极大结果，用于在存在下限限制的情况下估计加权平方误差损失下的均值。该发现恢复了结果已知的案例，以及其他新案例，例如负二项式模型。我们还研究了一个相关的自极小属性，获得了几个非极小极大的结果。最后，对于泊松和负二项式等离散模型，我们获得了均值下界限制的极小极大估计量类，其中包括范围保持解。