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Rate of convergence in the strong law of large numbers for a class of U-statistics and von Mises statistics

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  • Christofides, Tasos C.

Abstract

For the class of U-statistics based on multidimensionally indexed random variables introduced in Christofides (1987), an improved rate of convergence in the strong law of large numbers is obtained using martingale inequalities and other results. In addition, the same rate of convergence is obtained for the class of associated von Mises statistics.

Suggested Citation

  • Christofides, Tasos C., 1997. "Rate of convergence in the strong law of large numbers for a class of U-statistics and von Mises statistics," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 225-231, January.
    • Handle: RePEc:eee:stapro:v:31:y:1997:i:3:p:225-231
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    References listed on IDEAS

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    1. Christofides, Tasos C., 1990. "Rate of convergence in the strong law of large numbers for U-statistics based on a multidimensionally indexed array of random variables," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 267-272, March.
    2. P. Janssen, 1981. "Rate of convergence in the central limit theorem and in the strong law of large numbers for von mises statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 28(1), pages 35-46, December.
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