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Weighted Kolmogorov-Smirnov test: Accounting for the tails

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  • R'emy Chicheportiche
  • Jean-Philippe Bouchaud

Abstract

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximate limit solutions found originally in unrelated fields, first in [L. Turban, J. Phys. A 25, 127 (1992)] and later in [P. L. Krapivsky and S. Redner, Am. J. Phys. 64, 546 (1996)].

Suggested Citation

  • R'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "Weighted Kolmogorov-Smirnov test: Accounting for the tails," Papers 1207.7308, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1207.7308
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    Cited by:

    1. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2013. "Some applications of first-passage ideas to finance," Papers 1306.3110, arXiv.org.
    2. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    3. Kylie-Anne Richards & Gareth W. Peters & William Dunsmuir, 2015. "Heavy-tailed features and dependence in limit order book volume profiles in futures markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 1-56.
    4. Brzezinski, Michal, 2014. "Do wealth distributions follow power laws? Evidence from ‘rich lists’," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 155-162.
    5. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Ji, Lanpeng & Liu, Peng & Robert, Stephan, 2019. "Tail asymptotic behavior of the supremum of a class of chi-square processes," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.

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