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arXiv:1405.1791stat.AP

On the Super-Additivity and Estimation Biases of Quantile Contributions

Nassim N Taleb, Raphael Douady

Abstract

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.

arXiv comments
Journal reference
Physica A: Statistical Mechanics and its Applications 429, 252-260, 2015
DOI
doi:10.1016/j.physa.2015.02.038
Subjects
stat.APApplications (Statistics) q-fin.RMRisk Management q-fin.STStatistical Finance

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  1. Stephen Wolfram – 4-Hour Conversational Documentary on My Entire Arc of Life [video] 1 comment

    • Ok, the guy is not some Fields medalist, so it depends what you mean by math chops, but here are a few of his papers published in respectable journals that have non negligible math content: https://www.sciencedirect.com/science/article/abs/pii/S03784... (free at…

      leto_iiView on HNParent context

  2. Inequality and Skin in the Game 1 comment

    • Not what I said. I didn't say Piketty was correct, only that your assertion was unsupported by the evidence you presented. FYI, I believe this is the paper you were referring to: https://arxiv.org/pdf/1405.1791.pdf The gist of the paper as far as I can tell is that when sampling…

      vannevarView on HNParent context

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