Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications

The book investigates the misapplication of conventionalstatistical techniques to fat tailed distributions and looks forremedies, when possible.Switching from thin tailed to fat tailed distributions requiresmore than “changing the color of the dress.” Traditionalasymptotics deal mainly with either n=1 or n=∞, and the real worldis in between, under the “laws of the medium numbers”–which varywidely across specific distributions. Both the law of large numbersand the generalized central limit mechanisms operate in highlyidiosyncratic ways outside the standard Gaussian or Levy-Stablebasins of convergence.A few examples:The sample mean is rarely in line with the population mean,with effect on “naïve empiricism,” but can be sometimes beestimated via parametric methods.The “empirical distribution” is rarely empirical.Parameter uncertainty has compounding effects on statisticalmetrics.Dimension reduction (principal components) fails.Inequality estimators (Gini or quantile contributions) are notadditive and produce wrong results.Many “biases” found in psychology become entirely rationalunder more sophisticated probability distributions.Most of the failures of financial economics, econometrics, andbehavioral economics can be attributed to using the wrongdistributions.This book, the first volume of the Technical Incerto,weaves a narrative around published journal articles.