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摘要翻译：
本文讨论了两个密度的交点的估计，给出了两个密度的样本。这个问题是在分类理论中出现的。主要结果为估计误差在由样本容量的反立方根决定的尺度上的大概率提供了下界。作为推论，我们得到了分类问题中预测误差的概率界。证明的关键是熵估计。下界是基于一般估计量的界，一般估计量也适用于其他情况。此外，我们引入了一类误差渐近满足下界允许边界的最优估计。
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英文标题：
《Optimal third root asymptotic bounds in the statistical estimation of
thresholds》
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作者：
Franz Merkl, Leila Mohammadi
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/712.0894
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