英文标题：
《Cleaning large correlation matrices: tools from random matrix theory》
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作者：
Jo\\\"el Bun, Jean-Philippe Bouchaud and Marc Potters
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最新提交年份：
2016
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英文摘要：
  This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent \"Rotationally Invariant\" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.
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中文摘要：
本文综述了使用随机矩阵理论（RMT）工具估计大协方差矩阵的最新结果。我们介绍了几种RMT方法和分析技术，如复制形式主义和自由概率，重点介绍了Marchenko Pastur方程，该方程提供了关于乘性损坏的噪声矩阵的预解的信息。特别注意经验相关矩阵的特征向量的统计，这对于许多应用来说是至关重要的。我们特别展示了当底层过程的结构没有先验知识时，如何利用这些结果为大型相关矩阵构建一致的“旋转不变”估计量（RIE）。本综述的最后一部分以金融市场中的一些实际应用为例。我们从经验上证明了RIE框架的有效性，在这种情况下，该框架优于所有先前提出的方法。附加（而非乘法）损坏的噪声矩阵的情况也在一个特殊的附录中处理。本文讨论了几个开放性问题和有趣的技术发展。
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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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：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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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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