Lepto-Variance中的信息含量及其与高阶矩的关系
The Informational Content in Lepto-Variance and Its Relation to Higher Moments
- University of Limassol（利马索尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过模拟正态样本，研究lepto-variance的信息含量及其与方差、偏度、峰度的关系，发现其占总方差比例与超额峰度相关，且与偏度正交。
AI中文摘要：
Lepto回归被定义为对目标特征自身构建回归树的机器学习过程。它是一种新颖的、无模型的方法，可能揭示样本重要结构性质的信息。但目前尚不清楚lepto-variance的信息含量是什么，以及它与样本的其他已知统计量有何关系。一个重要的发现是，美国历史股票收益变异的58%是1比特的lepto-variance，这无法由任何金融因素解释。本文研究的核心问题是利用小的正态N(0,1)抽样样本，探索1比特样本lepto-variance和lepto-ratio与样本方差、偏度和超额峰度的关系。通过大样本模拟，发现正态分布的lepto-ratio收敛于36.3%。对于较小的正态分布模拟N(0,1)样本，虽然lepto-variance本身与样本方差高度相关，但lepto-variance占总方差的比例与超额峰度高度相关。lepto-variance和lepto-ratio均与样本偏度正交。另一个发现是，虽然lepto-ratio与lepto-variance强相关，但它与样本方差保持正交。
英文摘要：
Lepto-regression is defined as the machine learning process of constructing a Regression Tree of a target feature on itself. It is a novel, model-free method potentially revealing information on important sample structure properties. But it is yet not clear what the informational content of lepto-variance is and how it is related to other well-known statistics of a sample. One significant finding is that 58% of the historical US stock return variability is 1-bit lepto-variance that can not be explained by any financial factor. The central question investigated in this paper is to use small normal N(0, 1) drawn samples to explore how the 1-bit sample lepto-variance and lepto-ratio relate to sample variance, skewness and excess kurtosis. Using a large sample simulation, the lepto ratio of a normal is found to converge to 36.3%. For smaller normally distributed simulated N(0, 1) samples, while lepto-variance itself is highly correlated to sample variance, lepto-variance as a fraction of total variance is highly correlated to excess kurtosis. Both lepto-variance and lepto-ratio are orthogonal to sample skew. Another finding is that while lepto-ratio is strongly correlated to lepto-variance it remains orthogonal to sample variance.
