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On the unconditional strong law of large numbers for the bootstrap mean

Author

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  • Arenal-Gutiérrez, Eusebio
  • Matrán, Carlos
  • Cuesta-Albertos, Juan A.

Abstract

We first analyze some results by Athreya (1983) and Csörgo (1992). Then, by taking into account the different rates of convergence of the resampling size, we give new, simple proofs of those results. We provide examples that show that the sizes of resampling required by our results to ensure a.s. convergence are not far from being optimal.

Suggested Citation

  • Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "On the unconditional strong law of large numbers for the bootstrap mean," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 49-60, March.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:1:p:49-60
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    References listed on IDEAS

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    1. Burke, Murray D. & Gombay, Edit, 1988. "On goodness-of-fit and the bootstrap," Statistics & Probability Letters, Elsevier, vol. 6(5), pages 287-293, April.
    2. Athreya, K. B., 1983. "Strong law for the bootstrap," Statistics & Probability Letters, Elsevier, vol. 1(3), pages 147-150, March.
    3. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
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    Cited by:

    1. Hu, Tien-Chung & Ordóñez Cabrera, Manuel & Volodin, Andrei, 2005. "Asymptotic probability for the bootstrapped means deviations from the sample mean," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 178-186, September.
    2. Csörgő, Miklós & Nasari, Masoud M., 2013. "Asymptotics of randomly weighted u- and v-statistics: Application to bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 176-192.
    3. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.

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