Prediction Sufficiency When the Loss Function Does Not Depend on The Unknown Parameter
The Annals of Statistics · 1977 · Volume 5 · Issue 1
Abstract
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 conditions may be replaced by a condition of conditional independence for prior distributions.
Keywords
62B05, 62C07, conditional independence for prior distributions, minimal sufficiency, Prediction sufficiency
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