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On a paradoxical property of the Kolmogorov–Smirnov two-sample test

Alexander Y. Gordon and Lev B. Klebanov

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Abstract

The two-sample Kolmogorov–Smirnov test can lose power as the size of one sample grows while the size of the other sample remains constant. In this case, a paradoxical situation takes place: the use of additional observations weakens the ability of the test to reject the null hypothesis when it is false.

Chapter information

Source
J. Antoch, M. Hušková and P.K. Sen, eds., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 70-74

Dates
First available in Project Euclid: 29 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1291044743

Digital Object Identifier
doi:10.1214/10-IMSCOLL707

Mathematical Reviews number (MathSciNet)
MR2808367

Subjects
Primary: 62G10: Hypothesis testing

Keywords
Kolmogorov goodness-of-fit test Kolmogorov–Smirnov two-sample test unbiasedness

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Gordon, Alexander Y.; Klebanov, Lev B. On a paradoxical property of the Kolmogorov–Smirnov two-sample test. Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, 70--74, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL707. https://projecteuclid.org/euclid.imsc/1291044743


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References

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  • [4] Thompson, Roy O.R.Y (1966) Bias of the One-Sample Cramér-Von Mises Test. Journal of Amer. Statist. Association 61 246-247.