On the super-additivity and estimation biases of quantile contributions

Nassim Nicholas Taleb and Raphael Douady ()

Physica A: Statistical Mechanics and its Applications, 2015, vol. 429, issue C, 252-260

Abstract: Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to both sample and population 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, 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∪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.

Keywords: Quantile contribution; Measure of inequality; Estimation bias; Power law; Law of large number; Concentration measure (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (22)

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Related works:
Working Paper: On the Super-Additivity and Estimation Biases of Quantile Contributions (2015)
Working Paper: On the Super-Additivity and Estimation Biases of Quantile Contributions (2015)
Working Paper: On the Super-Additivity and Estimation Biases of Quantile Contributions (2014)
Working Paper: On the Super-Additivity and Estimation Biases of Quantile Contributions (2014)
Working Paper: On the Super-Additivity and Estimation Biases of Quantile Contributions (2014)
Working Paper: On the Super-Additivity and Estimation Biases of Quantile Contributions (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:429:y:2015:i:c:p:252-260

DOI: 10.1016/j.physa.2015.02.038

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