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A central limit theorem for two-sample U-processes

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  • Neumeyer, Natalie

Abstract

In this paper collections of two-sample U-statistics are considered as a U-process indexed by a class of kernels. Sufficient conditions for a functional central limit theorem in the non-degenerate case are given and a uniform law of large numbers is obtained. The conditions are in terms of random covering numbers and are, for example, fulfilled for Vapnik-Chervonenkis classes of functions.

Suggested Citation

  • Neumeyer, Natalie, 2004. "A central limit theorem for two-sample U-processes," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 73-85, March.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:1:p:73-85
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    References listed on IDEAS

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    1. Schneemeier, Wilhelm, 1989. "Weak convergence and Glivenko-Cantelli results for empirical processes of u-statistic structure," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 325-334, December.
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    Cited by:

    1. Hong, Han & Li, Huiyu & Li, Jessie, 2021. "BLP estimation using Laplace transformation and overlapping simulation draws," Journal of Econometrics, Elsevier, vol. 222(1), pages 56-72.
    2. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    3. M. Ahmad, 2014. "A $$U$$ -statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens–Fisher setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 33-61, February.
    4. Heikki Kauppi, 2016. "The Generalized Receiver Operating Characteristic Curve," Discussion Papers 114, Aboa Centre for Economics.

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