Distance-based and continuum Fano inequalities with applications to statistical estimation
Distance-based and continuum Fano inequalities with applications to statistical estimation
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基于距离的连续 Fano 不等式及其在统计估计中的应用
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Wainwright
中科院分区：
文献类型：
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作者：
John C. Duchi;M. Wainwright
在此技术说明中，我们给出了信息理论中经典的Fano不平等的两个扩展。第一个将Fano的不平等扩展到估计设置，从而提供了下限，即离散数量的估计器在数量的一定距离内$ t $。第二不平等将我们的界限扩展到连续设置，并提供基于音量的界限。我们说明这些不平等是如何导致几个统计最小型下限的直接和简单证明。
In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano's inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a discrete quantity is within some distance $t$ of the quantity. The second inequality extends our bound to a continuum setting and provides a volume-based bound. We illustrate how these inequalities lead to direct and simple proofs of several statistical minimax lower bounds.