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Almost sure limit theorems for U-statistics

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  • Holzmann, Hajo
  • Koch, Susanne
  • Min, Aleksey
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    Abstract

    We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki [(Stochastic Process. Appl. 94 (2001) 105)]. We extend this result to the case of convergence to stable laws and also prove a functional version.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 3 (September)
    Pages: 261-269

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    Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:261-269

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    Related research

    Keywords: Almost sure limit theorem Functional limit theorem Stable distributions U-statistics;

    References

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    1. M. Denker & C. Grillenberger & G. Keller, 1985. "A note on invariance principles for v. Mises' statistics," Metrika, Springer, vol. 32(1), pages 197-214, December.
    2. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    3. Neuhaus, Georg, 1977. "Functional limit theorems for U-statistics in the degenerate case," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 424-439, September.
    4. Heinrich, L. & Wolf, W., 1993. "On the Convergence of U-Statistics with Stable Limit Distribution," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 266-278, February.
    5. Berkes, István & Csáki, Endre, 2001. "A universal result in almost sure central limit theory," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 105-134, July.
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    Cited by:
    1. Zuoxiang Peng & Zhongquan Tan & Saralees Nadarajah, 2011. "Almost sure central limit theorem for the products of U-statistics," Metrika, Springer, vol. 73(1), pages 61-76, January.

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