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Almost sure limit theorems for U-statistics


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


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.

Suggested Citation

  • Holzmann, Hajo & Koch, Susanne & Min, Aleksey, 2004. "Almost sure limit theorems for U-statistics," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 261-269, September.
  • Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:261-269

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. M. Denker & C. Grillenberger & G. Keller, 1985. "A note on invariance principles for v. Mises' statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 197-214, December.
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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: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(1), pages 61-76, January.


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