Abstract

http://ssrn.com/abstract=2434363
 


 



On the Biases and Variability in the Estimation of Concentration Using Bracketed Quantile Contributions


Nassim Nicholas Taleb


New York University-Poly School of Engineering

Raphael Douady


Riskdata; CES Univ. Paris 1

May 7, 2014


Abstract:     
In fat-tailed domains, sample measures of top centile contributions to the total (concentration) are biased, unstable estimators extremely sensitive to sample size and concave in accounting for large deviations. They can vary over time merely from the increase of sample space, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as weighted concentration measures for A and B will tend to be lower than that from A+B. In addition, it can be shown that under fat tails, increases in the total sum need to be accompanied by increased measurement of concentration. We examine the bias and error under straight and mixed distributions.

Number of Pages in PDF File: 5

Keywords: Risk, Inequality, Statistics

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Date posted: May 9, 2014  

Suggested Citation

Taleb, Nassim Nicholas and Douady, Raphael, On the Biases and Variability in the Estimation of Concentration Using Bracketed Quantile Contributions (May 7, 2014). Available at SSRN: http://ssrn.com/abstract=2434363 or http://dx.doi.org/10.2139/ssrn.2434363

Contact Information

Nassim Nicholas Taleb (Contact Author)
New York University-Poly School of Engineering ( email )
Brooklyn, NY 11201
United States

Raphael Douady
Riskdata ( email )
6, rue de l'Amiral Coligny
Paris, 75001
France
HOME PAGE: http://www.riskdata.com
CES Univ. Paris 1 ( email )
106 bv de l'Hôpital
Paris, 75013
France
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