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Weighted Kolmogorov-Smirnov test: Accounting for the tails

Rémy Chicheportiche1,2 and Jean-Philippe Bouchaud1

  • 1Capital Fund Management, 75 007 Paris, France
  • 2Chaire de finance quantitative, Ecole Centrale Paris, 92 295 Châtenay-Malabry, France

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Phys. Rev. E 86, 041115 – Published 10 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041115

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)].

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Phys. Rev. E 86, 041115– Published 10 October, 2012
  • Received 1 August 2012

©2012 American Physical Society

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