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Bounds for the uniform deviation of empirical measures

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  • Devroye, Luc

Abstract

If X1,...,Xn are independent identically distributed Rd-valued random vectors with probability measure [mu] and empirical probability measure [mu]n, and if is a subset of the Borel sets on Rd, then we show that P{supA[set membership, variant][mu]n(A)-[mu](A)>=[var epsilon]}

Suggested Citation

  • Devroye, Luc, 1982. "Bounds for the uniform deviation of empirical measures," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 72-79, March.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:1:p:72-79
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    Citations

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    Cited by:

    1. Ryan Cumings-Menon, 2022. "Differentially Private Estimation via Statistical Depth," Papers 2207.12602, arXiv.org.
    2. Bartlett, Peter & Lugosi, Gábor, 1999. "An inequality for uniform deviations of sample averages from their means," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 55-62, August.
    3. Pal, Soumik, 2007. "Computing strategies for achieving acceptability: A Monte Carlo approach," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1587-1605, November.
    4. Levon Demirdjian & Majid Mojirsheibani, 2019. "Kernel classification with missing data and the choice of smoothing parameters," Statistical Papers, Springer, vol. 60(5), pages 1487-1513, October.
    5. Xu, Jianjun & Tan, Xianming & Zhang, Runchu, 2010. "A note on Phillips (1991): "A constrained maximum likelihood approach to estimating switching regressions"," Journal of Econometrics, Elsevier, vol. 154(1), pages 35-41, January.
    6. Luc Devroye & Gábor Lugosi & Frederic Udina, 1998. "Inequalities for a new data-based method for selecting nonparametric density estimates," Economics Working Papers 281, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Lugosi, Gábor, 1995. "Improved upper bounds for probabilities of uniform deviations," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 71-77, October.

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