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Some measures of kurtosis and their inference on large datasets

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  • Claudio Giovanni Borroni

    (University of Milano-Bicocca)

  • Lucio De Capitani

    (University of Milano-Bicocca)

Abstract

This paper deals with the estimation of kurtosis on large datasets. It aims at overcoming two frequent limitations in applications: first, Pearson's standardized fourth moment is computed as a unique measure of kurtosis; second, the fact that data might be just samples is neglected, so that the opportunity of using suitable inferential tools, like standard errors and confidence intervals, is discarded. In the paper, some recent indexes of kurtosis are reviewed as alternatives to Pearson’s standardized fourth moment. The asymptotic distribution of their natural estimators is derived, and it is used as a tool to evaluate efficiency and to build confidence intervals. A simulation study is also conducted to provide practical indications about the choice of a suitable index. As a conclusion, researchers are warned against the use of classical Pearson’s index when the sample size is too low and/or the distribution is skewed and/or heavy-tailed. Specifically, the occurrence of heavy tails can deprive Pearson’s index of any meaning or produce unreliable confidence intervals. However, such limitations can be overcome by reverting to the reviewed alternative indexes, relying just on low-order moments.

Suggested Citation

  • Claudio Giovanni Borroni & Lucio De Capitani, 2022. "Some measures of kurtosis and their inference on large datasets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 573-607, December.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:4:d:10.1007_s10182-022-00442-y
    DOI: 10.1007/s10182-022-00442-y
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    References listed on IDEAS

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