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Necessary and sufficient conditions for the moving blocks bootstrap central limit theorem of the mean

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  • Dragan Radulović

Abstract

For strictly stationary sequences Xi, we study the relations between statistics Zn=n−1/2∑ (Xi−EXi) and its Bootstrap counterpart We establish sufficient and necessary conditions for Central Limit Theorem in this setting and generalise the cases for which converges to Gaussian limit, while Zn fails to do so. In addition, we establish Bootstrap Central Limit Theorem without mixing conditions and identify the cases for which and Zn are asymptotically close, while both fail to converge in distribution.

Suggested Citation

  • Dragan Radulović, 2012. "Necessary and sufficient conditions for the moving blocks bootstrap central limit theorem of the mean," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 343-357.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:343-357
    DOI: 10.1080/10485251003663517
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    Cited by:

    1. El Ktaibi, Farid & Gail Ivanoff, B. & Weber, Neville C., 2014. "Bootstrapping the empirical distribution of a linear process," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 134-142.
    2. Dominik Wied, 2017. "A nonparametric test for a constant correlation matrix," Econometric Reviews, Taylor & Francis Journals, vol. 36(10), pages 1157-1172, November.
    3. Schweer, Sebastian & Wichelhaus, Cornelia, 2015. "Nonparametric estimation of the service time distribution in the discrete-time GI/G/∞ queue with partial information," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 233-253.

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