Almost sure limit theorems for U-statistics
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.
Volume (Year): 69 (2004)
Issue (Month): 3 (September)
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- 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.
- 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.
- 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.
- 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.
- 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.
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