测量预算约束下的Pinsker界：最优分配
Pinsker bound under measurement budget constrain: optimal allocation
摘要：
在经典的许多正常的手段，不同的方差，我们考虑的情况下，观察员被允许分配可用的测量预算的坐标的参数的兴趣。基准是一个集合上的极小极大线性风险。我们解决了两种类型的集合，椭球和超矩形的测量预算约束下的最优分配问题的观察。通过详细说明两个例子的索伯列夫椭球和hyperectangles，我们演示了如何重新分配测量（次）最优的方式提高了标准的均匀分配。特别地，我们改进了著名的Pinsker（1980）界。
英文摘要：
In the classical many normal means with different variances, we consider the situation when the observer is allowed to allocate the available measurement budget over the coordinates of the parameter of interest. The benchmark is the minimax linear risk over a set. We solve the problem of optimal allocation of observations under the measurement budget constrain for two types of sets, ellipsoids and hyperrectangles. By elaborating on the two examples of Sobolev ellipsoids and hyperectangles, we demonstrate how re-allocating the measurements in the (sub-)optimal way improves on the standard uniform allocation. In particular, we improve the famous Pinsker (1980) bound.
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