Background:
The
technical papers below are part of a systematic approach to uncover
mismeasurement of statistical estimators under fattailedness and
propose corrections and alternative tools. Conventional statistics fail
to cover fat tails; physicists who use power laws do not usually
produce statistical estimators, leading to a large —and consequential
— gap. It is not just changing the color of the dress (see discussion below). The initial aim was to establish a network of Bourbaki-style collaborators in a synchronized way working on the gap and injecting rigor in policy-making and decision-making under fat tails. Taleb, N.N., "The law of large numbers under fat tails"(in progress). This the central idea; it shows where statistical inference is BS and explores more rigorous estimation of the mean of the sum of fat-tailed random variables. A YouTube presentation here at MIT Big Data Luncheon. The inequality papers (apply to all measures of concentration, not just inequality): The
next two papers apply the
idea showing the flaw in using "averages" and "sums" as estimators of
inequality under fat tails, instead of maximum likelihood methods
applied to the tail exponent. Measurements of changes in inequality we
have recently witnessed (triggering active discussions) are based on
unrigorous methods; seen from these metrics, changes in inequality can
be either overly underestimated or severely exaggerated (particularly
those concerning wealth which has much fatter tails than income).
Taleb, N. N. and Douady, R., 2015, "On the super- additivity and estimation biases of quantile contributions" Physica A: Statistical Mechanics and Applications proves that measures of concentration (e.g. "top 1% has 50% of wealth"، "top 1% of wars killed 50% of people") are size dependent and aggregate poorly. Taleb, N.N., "How to (not) estimate Gini indices for fat tailed variables". The paper shows a severe but more tractable problem with the Gini and proposes efficient unbiased estimators, deriving their properties. Some have argued that "it is only a problems for fat tails" except that Gini is a measure for fat tailedness. Milanovic, B. and Taleb, N.N. Why the super-rich care more about inequality than growth. In Progress.
The dual distribution papers: techniques that help finding the "true (or shadow) mean" as opposed to the sample mean. Cirillo, P. and Taleb, N.N.,
2016, "On the statistical
properties and tail risk of violent conflicts" (Physica A). Yes, the thesis by the science writer S.
Pinker on the "drop in violence" has no statistical basis. Under fat
tails, sample means are unstable and underestimate true means. The
paper proposes a method to use dual distributions, removing compact
support to apply Extreme Value Theory, and transfer parameters to the primal. Also a
novel robust approach to unreliable estimators.
Taleb, N.N., Cirillo and P., Taleb, N.N., 2016,"Expected shortfall estimation for apparently infinite-mean models of operational risk", under revision, Quantitative Finance Option Theory Taleb, N.N., 2015, Unique Option Pricing Measure
with neither Dynamic Hedging nor Complete Markets, European Financial
Management . It proves
using measure theory how a distribu- tion with finite first moment can
produce a risk-neutral option price, and why we can dispense with both
the dynamic hedging and pricing kernel arguments –hence price options
with fat-tails.
Formalization of the barbell strategy using information theory We are clueless about downside probability, particularly under fat tails. We look at constructions with severe tail constraints and compatible with gambler's ruin (a generalization of Kelly's criterion). Geman, D., Geman, H. and
Taleb, N.N., 2015. "Tail risk
constraints and maximum entropy". Entropy,
17, pp.1-14.
Dimensionality and Model Error Taleb, N.N., "Model
error and dimensionality". In progress
Undecidability: amply covered in Silent Risk (it is its theme), here is the formalization. Douady, R. and Taleb, N.N. Statistical Undecidability Under
what conditions on the metadistribution of the probability measure is a
statistical formally decidable.
Power laws and stochastic tail Exponents mixtures of power laws. TBA
Some BS detecting papers Taleb, N.N., 2014, (On The conflation of long volatility and fat tails), Quantitative Finance. A strange overactive smear-campaigner, Eric Falkenstein, extremely innocent of probability, kept spreading all manner of disinformation about my work. While it may have been ineffective in stopping the spread of my ideas, the strawmanship resulted in people mistaking the tails with the scale of the distribution. This is meant to correct. It is not changing the color of the dress Many people know (well, sort of) what fat tails means, but in a vague sense, believing that it is just another class of distributions than the normal and they can think of them as, simply, other distributions doing the same thing. Unfortunately things work differently: The very definition of inference and confidence interval goes out of the window. More rigor is required. To work with fat tails one has to approach things differently, at a conceptual level. In fact one of us found contradictions in discussions: once it is stated that a distributions is fat-tailed, then many statements taken for granted are no longer valid. • The mean of the distribution will not
correspond to the sample mean. In fact there is no fat-tailed
distribution in which the mean can be properly estimated from the
sample mean.
• Sharpe ratio, variance, beta and other common fi- nance metrics are uninformative. Variance and stan- dard deviations are not useable. • Correlations (in the Pearson sense) usually do not exist, and when they do, provide little information (but there are other forms of dependence). • Robust statistics is not robust at all. • Maximum likelihood methods work for parameters (good news). • The gap between disconfirmatory and confirmatory empiricism is wider than common statistics. • Principal components analysis is likely to produce false factors. • Methods of moments fail to work. • There is no such thing as "typical" large deviation: conditional on having a large move, such move isn’t defined |
Silent
Risk, a book in progress
(freely available PDF, ~500 pages). N. N. Taleb's Home Page Precautionary Principle Page Real World Risk Institute The fragility heuristic paper (with IMF, non technical) A Mathematical Formulation of (Anti)Fragility (technical) Skin In the Game Page |