标题： 基于阈值的质量度量的最优估计量 显示英文标题

标题： Optimal estimators for threshold-based quality measures

摘要： 我们考虑一个参数估计问题：给定来自未知分布的$n$个样本，我们想要估计这些数据是从给定的一参数族中产生的哪个分布。 按照 Schulman 和 Vazirani 的方法，我们根据在最坏情况下处于正确答案指定容差内的概率来评估估计器。 我们为$\mathbb{R}$上的几个分布族提供了最优估计器。 我们证明对于紧致空间上的分布，总存在一个平移不变的最优估计器，并且我们猜想这一结论也适用于$\mathbb{R}$上的任何分布。 相比之下，我们给出一个例子说明在无限树上的某种分布上这一结论不成立。 显示英文摘要

摘要： We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an estimator in terms of the chance of being within a specified tolerance of the correct answer, in the worst case. We provide optimal estimators for several families of distributions on $\mathbb{R}$. We prove that for distributions on a compact space, there is always an optimal estimator that is translation-invariant, and we conjecture that this conclusion also holds for any distribution on $\mathbb{R}$. By contrast, we give an example showing it does not hold for a certain distribution on an infinite tree.