标题： 具有给定均值和方差的Hellinger距离的紧下界 显示英文标题

标题： A Tight Lower Bound for the Hellinger Distance with Given Means and Variances

摘要： 二元散度是指在相同二元集合上定义的概率测度之间的散度，具有一种有趣的性质。 对于卡方散度和相对熵，已知它们的二元散度分别在给定均值和方差的情况下达到下界。 在本文中，我们证明了平方Hellinger距离的二元散度具有相同的性质，并提出一个开放问题，即f散度需要满足什么条件才能具备这一性质。 显示英文摘要

摘要： The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain lower bounds with given means and variances, respectively. In this note, we show that the binary divergence of the squared Hellinger distance has the same property and propose an open problem that what conditions are needed for f-divergence to satisfy this property.