英文标题：
《The Perfect Marriage and Much More: Combining Dimension Reduction,
  Distance Measures and Covariance》
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作者：
Ravi Kashyap
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最新提交年份：
2019
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英文摘要：
  We develop a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions of random variables, and the Johnson-Lindenstrauss Lemma, a technique for dimension reduction. The resulting technique is a simple yet powerful tool that allows comparisons between data-sets representing any two distributions. The degree to which different entities, (markets, universities, hospitals, cities, groups of securities, etc.), have different distance measures of their corresponding distributions tells us the extent to which they are different, aiding participants looking for diversification or looking for more of the same thing. We demonstrate a relationship between covariance and distance measures based on a generic extension of Stein\'s Lemma. We consider an asset pricing application and then briefly discuss how this methodology lends itself to numerous market-structure studies and even applications outside the realm of finance / social sciences by illustrating a biological application. We provide numerical illustrations using security prices, volumes and volatilities of both these variables from six different countries.
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中文摘要：
我们基于Bhattacharyya距离和Johnson-Lindenstrauss引理（降维技术）之间的结合，开发了一种新的方法。由此产生的技术是一个简单但功能强大的工具，可以在代表任意两种分布的数据集之间进行比较。不同实体（市场、大学、医院、城市、证券集团等）对其相应分布的不同距离度量的程度告诉我们它们的不同程度，有助于参与者寻求多样化或寻找更多相同的东西。基于Stein引理的一般扩展，我们证明了协方差和距离度量之间的关系。我们考虑一个资产定价应用，然后通过举例说明一个生物应用，简要讨论该方法如何适用于大量市场结构研究，甚至金融/社会科学领域之外的应用。我们使用六个不同国家的证券价格、交易量和这两个变量的波动率提供了数字说明。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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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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