用f散度给出假设检验边界的新下界，改进了皮尔斯克不等式。
Bounding Neyman-Pearson Region with $f$-Divergences
- 基于任意f散度构建假设检验边界的紧下界。
- 在KL散度下优于皮尔斯克不等式，且可导出闭式上界。
- 提出构造分布对以精确或近似实现目标检验边界的方法。
简单二元假设检验的Neyman-Pearson区域是所有检验对应的假阳性率与假阴性率构成的点集。该区域的下边界由Neyman-Pearson引理给出，经坐标变换后等价于最优ROC曲线。本文建立了基于任意f-散度的边界新下界；其中，曲棍球棒型f散度生成的下界能精确刻画Neyman-Pearson边界，因此为最优。当采用KL散度时，该下界改进了经典的Pinsker不等式。此外，我们还得到了基于Chernoff α系数的闭式精化上界。最后，提出了构造分布对以近似或精确实现任意给定Neyman-Pearson边界的算法。
原文摘要 · Abstract (English)
The Neyman-Pearson region of a simple binary hypothesis testing is the set of points whose coordinates represent the false positive rate and false negative rate of some test. The lower boundary of this region is given by the Neyman-Pearson lemma, and is up to a coordinate change, equivalent to the optimal ROC curve. We establish a novel lower bound for the boundary in terms of any $f$-divergence. Since the bound generated by hockey-stick $f$-divergences characterizes the Neyman-Pearson boundary, this bound is best possible. In the case of KL divergence, this bound improves Pinsker's inequality. Furthermore, we obtain a closed-form refined upper bound for the Neyman-Pearson boundary in terms of the Chernoff $α$-coefficient. Finally, we present methods for constructing pairs of distributions that can approximately or exactly realize any given Neyman-Pearson boundary.
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