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On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality

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  • Naaman, Michael

Abstract

We derive the tight constant in the multivariate version of the Dvoretzky–Kiefer–Wolfowitz inequality. The inequality is leveraged to construct the first fully non-parametric test for multivariate probability distributions including a simple formula for the test statistic. We also generalize the test under appropriate α-mixing conditions and describe applications of the tests to machine learning and representative sampling.

Suggested Citation

  • Naaman, Michael, 2021. "On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:stapro:v:173:y:2021:i:c:s016771522100050x
    DOI: 10.1016/j.spl.2021.109088
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    References listed on IDEAS

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    1. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    2. Devroye, Luc P., 1977. "A uniform bound for the deviation of empirical distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 594-597, December.
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    Cited by:

    1. Sloot Henrik, 2022. "Implementing Markovian models for extendible Marshall–Olkin distributions," Dependence Modeling, De Gruyter, vol. 10(1), pages 308-343, January.
    2. Jiafei Huan & Li Deng & Yue Zhu & Shangguang Jiang & Fei Qi, 2024. "Short-to-Medium-Term Wind Power Forecasting through Enhanced Transformer and Improved EMD Integration," Energies, MDPI, vol. 17(10), pages 1-22, May.
    3. Anderson, William & Farazmand, Mohammad, 2024. "Fisher information and shape-morphing modes for solving the Fokker–Planck equation in higher dimensions," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    4. Nicol`o Cesa-Bianchi & Tommaso Cesari & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2021. "Bilateral Trade: A Regret Minimization Perspective," Papers 2109.12974, arXiv.org.
    5. Young Shin Kim & Hyun-Gyoon Kim, 2024. "Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence," Papers 2402.17919, arXiv.org, revised Mar 2024.

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