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固定或缩放半径置信集：固定样本量情形AI 解读

Confidence sets in the form of balls of fixed or scaled radius with respect to an arbitrary pseudometric are considered. Easily computable lower bounds for the radius of these confidence sets are derived. As by-products, bounds for the minimax risk are given and a method of deriving multiple decision procedures from point estimators is obtained.

密度函数及其导数估计的界AI 解读

Lower bounds on the radius of various confidence sets for density functions and their derivatives are determined. In each case investigated, the smallest radius obtainable and the radius actually obtained by using known estimates exhibit the same dependency on the fixed sample size $n$. The lower bounds are derived using methods in Meyer (1976). Although only a few combinations of pseudometric and density class are considered here, the techniques illustrated can be used…