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相对于完全信息与完全无信息的统计信息度量AI 解读

Two measures of content of information in statistical experiments are considered. They are both based on Le Cam's notion of deficiency of one experiment with respect to another. The measures are: (i) The deficiency of the given experiment with respect to a totally informative experiment. (ii) The deficiency of a totally uninformative experiment with respect to the given experiment. We shall here discuss the interpretations of such measures, establish inequalities for them…

损失函数不依赖未知参数时的预测充分性AI 解读

It is shown by Takeuchi and Akahira, 1974, that conditional independence together with a condition of "partial sufficiency" imply "prediction sufficiency" for loss functions not depending on the unknown parameter. We shall here prove that these conditions are necessary as well and thereby obtain a complete description, in terms of conditional expectations, of "prediction sufficiency" for loss functions not depending on the unknown parameter. It turns out that these…