On the Biases and Variability in the Estimation of Concentration Using Bracketed Quantile Contributions
Nassim Nicholas Taleb
New York University-Poly School of Engineering
Riskdata; CES Univ. Paris 1
May 7, 2014
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, Statisticsworking papers series
Date posted: May 9, 2014
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