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Finite sampling inequalities: An application to two-sample Kolmogorov–Smirnov statistics

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  • Greene, Evan
  • Wellner, Jon A.

Abstract

We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2012) concerning exponential bounds for two-sided Kolmogorov–Smirnov statistics by giving corresponding results for one-sided statistics with emphasis on “adjusted” inequalities of the type proved originally by Dvoretzky et al. (1956) [3] and by Massart (1990) for one-sample versions of these statistics.

Suggested Citation

  • Greene, Evan & Wellner, Jon A., 2016. "Finite sampling inequalities: An application to two-sample Kolmogorov–Smirnov statistics," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3701-3715.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:12:p:3701-3715
    DOI: 10.1016/j.spa.2016.04.020
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    References listed on IDEAS

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    1. Hush, Don & Scovel, Clint, 2005. "Concentration of the hypergeometric distribution," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 127-132, November.
    2. León, Carlos A. & Perron, François, 2003. "Extremal properties of sums of Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 345-354, May.
    3. Wei, Fan & Dudley, Richard M., 2012. "Two-sample Dvoretzky–Kiefer–Wolfowitz inequalities," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 636-644.
    4. Ehm, Werner, 1991. "Binomial approximation to the Poisson binomial distribution," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 7-16, January.
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