标题： 关于与Hellinger距离相关的鲁棒假设检验 显示英文标题

标题： On Robust hypothesis testing with respect to Hellinger distance

摘要： 我们研究假设检验问题，其中观察到的样本不必来自指定的任何一个假设（分布）。 在这种情况下，我们希望我们的检验对这种误设具有鲁棒性，并输出在Hellinger距离上更接近的分布。 如果底层分布接近等距于假设，则这将不可能实现。 我们的主要结果是量化底层分布必须与哪一个假设多接近。 我们还研究了复合检验问题，其中每个假设是一个固定分布周围的Hellinger球。 已知广义似然比检验适用于这个问题。 我们给出了一个替代检验方法。 显示英文摘要

摘要： We study the hypothesis testing problem where the observed samples need not come from either of the specified hypotheses (distributions). In such a situation, we would like our test to be robust to this misspecification and output the distribution closer in Hellinger distance. If the underlying distribution is close to being equidistant from the hypotheses, then this would not be possible. Our main result is quantifying how close the underlying distribution has to be to either of the hypotheses. We also study the composite testing problem, where each hypothesis is a Hellinger ball around a fixed distribution. A generalized likelihood ratio test is known to work for this problem. We give an alternate test for the same.