论文标题
来自得分变量阈值测试的最佳ROC曲线
Optimal ROC Curves from Score Variable Threshold Tests
论文作者
论文摘要
接收器操作特征（ROC）是二进制假设测试中检测和错误警报概率之间的权衡方面的完善表示。在许多实际情况下，ROC是通过阈值测量得分变量生成的 - 应用得分变量阈值测试（SVT）。在许多情况下，所得曲线与可能性比测试（LRT）ROC不同，因此不是Neyman-Pearson的最佳选择。虽然人们对ROC成为Neyman-Pearson最佳的必要条件是一个充分理解的，但本文确定，在使用SVT生成ROC的情况下，它也是足够的条件。它进一步定义了一个建设性的过程，可以通过该过程从非cove svt ROC生成LRT ROC，而无需明确了解得分变量的条件PDF。如果已知有条件的PDF，则该过程隐含地提供了一种重新设计测试的方法，使其等同于LRT。
The Receiver Operating Characteristic (ROC) is a well-established representation of the tradeoff between detection and false alarm probabilities in binary hypothesis testing. In many practical contexts ROC's are generated by thresholding a measured score variable -- applying score variable threshold tests (SVT's). In many cases the resulting curve is different from the likelihood ratio test (LRT) ROC and is therefore not Neyman-Pearson optimal. While it is well-understood that concavity is a necessary condition for an ROC to be Neyman-Pearson optimal, this paper establishes that it is also a sufficient condition in the case where the ROC was generated using SVT's. It further defines a constructive procedure by which the LRT ROC can be generated from a non-concave SVT ROC, without requiring explicit knowledge of the conditional PDF's of the score variable. If the conditional PDF's are known, the procedure implicitly provides a way of redesigning the test so that it is equivalent to an LRT.
