摘要翻译：
本文提出了一种确定随机变量X和Y的均值之比E(Y)/E(X)置信集的几何方法，该方法将构造两个随机变量之比的置信集问题简化为构造一维随机变量均值的置信集问题。它在许多情况下都是有效的。在正态分布随机变量的情况下，所构造的置信度集与标准Fieller置信度集相吻合。我们的构造的推广导致了对于非常一般的分布类的精确和保守置信集的定义，只要(X，Y)的联合期望存在并且形式为aX+bY的线性组合是良好的。最后，我们的几何方法允许导出一个非常简单的bootstrap方法来构造比率的保守置信集，这些置信集在某些情况下表现良好，特别是在非对称重尾区。
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英文标题：
《A Geometric Approach to Confidence Sets for Ratios: Fieller's Theorem,
  Generalizations, and Bootstrap》
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作者：
Ulrike von Luxburg, Volker H. Franz
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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：
  We present a geometric method to determine confidence sets for the ratio E(Y)/E(X) of the means of random variables X and Y. This method reduces the problem of constructing confidence sets for the ratio of two random variables to the problem of constructing confidence sets for the means of one-dimensional random variables. It is valid in a large variety of circumstances. In the case of normally distributed random variables, the so constructed confidence sets coincide with the standard Fieller confidence sets. Generalizations of our construction lead to definitions of exact and conservative confidence sets for very general classes of distributions, provided the joint expectation of (X,Y) exists and the linear combinations of the form aX + bY are well-behaved. Finally, our geometric method allows to derive a very simple bootstrap approach for constructing conservative confidence sets for ratios which perform favorably in certain situations, in particular in the asymmetric heavy-tailed regime.
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PDF链接：
https://arxiv.org/pdf/711.0198