肥尾的统计后果：现实世界的预渐近性、认识论与应用
Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications
AI总结：
本专著研究传统统计技术在肥尾分布中的误用问题，揭示了在现实预渐近条件下大数定律和中心极限机制的特异表现，并通过多领域实例指出错误分布导致的估计失效与认知偏差。
摘要：
（第三版纠正了微小的排版错误，增加了3个综合自已发表论文的章节，以及一个关于最大熵分布的附录。）本专著研究了对肥尾分布误用传统统计技术的问题，并在可能的情况下寻找补救措施。从薄尾分布切换到肥尾分布需要的不仅仅是“换件衣服的颜色”。传统的渐近理论主要处理 n=1 或 n=∞ 的情况，而现实世界介于两者之间，受“中数定律”的支配——这些定律在不同的具体分布中差异很大。大数定律和广义中心极限机制在标准的 Gaussian 或 Levy-Stable 收敛域之外，都以高度特异的方式运作。几个例子：样本均值很少与总体均值一致，这影响了“朴素经验主义”，但有时可以通过参数方法进行估计。“经验分布”很少是经验的。参数不确定性对统计指标有复合效应。降维（主成分）失效。不平等估计量（GINI 或分位数贡献）不可加，并产生错误结果。心理学中发现的许多“偏差”在更复杂的概率分布下变得完全理性。金融经济学、计量经济学和行为经济学的大部分失败都可归因于使用了错误的分布。本书是 Technical Incerto 的第一卷，围绕已发表的期刊文章编织了一段叙述。
英文摘要：
(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress". Traditional asymptotics deal mainly with either n=1 or $n=\infty$, and the real world is in between, under of the "laws of the medium numbers" --which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: + The sample mean is rarely in line with the population mean, with effect on "naive empiricism", but can be sometimes be estimated via parametric methods. + The "empirical distribution" is rarely empirical. + Parameter uncertainty has compounding effects on statistical metrics. + Dimension reduction (principal components) fails. + Inequality estimators (GINI or quantile contributions) are not additive and produce wrong results. + Many "biases" found in psychology become entirely rational under more sophisticated probability distributions + Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
