Abstract: The book 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.
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文明之光（第二册）
吴军 / 人民邮电出版社 / 2014-6 / 59.00元
【《文明之光》系列荣获由中宣部、中国图书评论学会和中央电视台联合推选的2014“中国好书”奖】 吴军博士从对人类文明产生了重大影响却在过去被忽略的历史故事里，选择了有意思的几十个片段特写，以人文和科技、经济结合的视角，有机地展现了一幅人类文明发展的宏大画卷。 《文明之光 》系列大致按照从地球诞生到近现代的顺序讲述了人类文明进程的各个阶段，每个章节相对独立，全景式地展现了人类文明发展历程......一起来看看 《文明之光（第二册）》 这本书的介绍吧!
