标题： 阈值统计估计中的最优三次方根渐近界 显示英文标题

标题： Optimal third root asymptotic bounds in the statistical estimation of thresholds

摘要： 本文研究了在给定两个密度样本的情况下估计这两个密度的交点问题。 该问题出现在分类理论中。 主要结果是在由样本大小的立方根倒数决定的比例上，提供了估计误差较大的概率的下界。 作为推论，我们得到了分类问题中预测误差的概率界。 证明的关键在于熵估计。 这些下界基于一般估计器的界，这些界也可用于其他上下文中。 此外，我们引入了一类最优估计器，其误差渐近达到由下界允许的边界。 显示英文摘要

摘要： This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the estimation errors to be large on a scale determined by the inverse cube root of the sample size. As corollaries, we obtain probabilistic bounds for the prediction error in a classification problem. The key to the proof is an entropy estimate. The lower bounds are based on bounds for general estimators, which are applicable in other contexts as well. Furthermore, we introduce a class of optimal estimators whose errors asymptotically meet the border permitted by the lower bounds.