论文标题
Hoeffding样假设检验的二阶渐近学检验
Second-Order Asymptotics of Hoeffding-Like Hypothesis Tests
论文作者
论文摘要
我们考虑了二进制统计假设测试问题，其中$ n $独立和相同分布的随机变量$ z^n $是根据零假设$ p $分配的，或者是替代假设$ q $，并且仅知道$ p $。对于这个问题，一个众所周知的测试是Hoeffding测试，如果$ z^n $和$ p $之间的kullback-leibler（kl）差异低于某个阈值，则接受$ p $。在本文中，我们考虑了类似于Hoeffding的测试，其中KL差异被其他差异替换，并为大量的差异表征了固定类型I错误的II型误差的一阶和二阶项。由于所考虑的类包括KL差异，因此我们获得了HOFERIDIDES测试的二阶项作为特殊情况。
We consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternate hypothesis $Q$, and only $P$ is known. For this problem, a well-known test is the Hoeffding test, which accepts $P$ if the Kullback-Leibler (KL) divergence between the empirical distribution of $Z^n$ and $P$ is below some threshold. In this paper, we consider Hoeffding-like tests, where the KL divergence is replaced by other divergences, and characterize, for a large class of divergences, the first and second-order terms of the type-II error for a fixed type-I error. Since the considered class includes the KL divergence, we obtain the second-order term of the Hoeffiding test as a special case.
