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A Glivenko-Cantelli theorem for empirical measures of independent but non-identically distributed random variables

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  • Wellner, Jon A.

Abstract

The bounded-dual-Lipschitz and Prohorov distances from the 'empirical measure' to the 'average measure' of independent random variables converges to zero almost surely if the sequence of average measures is tight. Three examples are also given.

Suggested Citation

  • Wellner, Jon A., 1981. "A Glivenko-Cantelli theorem for empirical measures of independent but non-identically distributed random variables," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 309-312, August.
    • Handle: RePEc:eee:spapps:v:11:y:1981:i:3:p:309-312
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    Cited by:

    1. Atı̇la Abdulkadı̇roğlu & Joshua D. Angrist & Yusuke Narita & Parag Pathak, 2022. "Breaking Ties: Regression Discontinuity Design Meets Market Design," Econometrica, Econometric Society, vol. 90(1), pages 117-151, January.
    2. Xiaoyu Cheng, 2022. "Robust Data-Driven Decisions Under Model Uncertainty," Papers 2205.04573, arXiv.org.
    3. Ning Xu & Jian Hong & Timothy C. G. Fisher, 2016. "Finite-sample and asymptotic analysis of generalization ability with an application to penalized regression," Papers 1609.03344, arXiv.org, revised Sep 2016.
    4. Atila Abdulkadiroglu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Impact Evaluation in Matching Markets with General Tie-Breaking," NBER Working Papers 24172, National Bureau of Economic Research, Inc.
    5. Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "Unconditional Glivenko-Cantelli-type theorems and weak laws of large numbers for bootstrap," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 365-375, March.

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