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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Lugosi, Gábor, 1995. "Improved upper bounds for probabilities of uniform deviations," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 71-77, October.
    7. 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.

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