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Approximations for weighted bootstrap processes with an application

Author

Listed:
  • Horváth, Lajos
  • Kokoszka, Piotr
  • Steinebach, Josef

Abstract

Let [beta]n(t) denote the weighted (smooth) bootstrap process of an empirical process. We show that the order of the best Gaussian approximation for [beta]n(t) is n-1/2 log n and we construct a sequence of approximating Brownian bridges achieving this rate. We also obtain an approximation for [beta]n(t) using a suitably chosen Kiefer process. The result is applied to detect a possible change in the distribution of independent observations.

Suggested Citation

  • Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 2000. "Approximations for weighted bootstrap processes with an application," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 59-70, May.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:1:p:59-70
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    References listed on IDEAS

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    1. Horváth, Lajos & Steinebach, Josef, 1999. "On the best approximation for bootstrapped empirical processes," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 117-122, January.
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    Cited by:

    1. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    2. Liu, Bo & Mojirsheibani, Majid, 2015. "On a weighted bootstrap approximation of the Lp norms of kernel density estimators," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 65-73.
    3. Sergio Alvarez-Andrade & Salim Bouzebda, 2014. "Asymptotic results for hybrids of empirical and partial sums processes," Statistical Papers, Springer, vol. 55(4), pages 1121-1143, November.
    4. Ali Al-Sharadqah & Majid Mojirsheibani, 2020. "A simple approach to construct confidence bands for a regression function with incomplete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 81-99, March.
    5. Mojirsheibani, Majid, 2012. "A weighted bootstrap approximation of the maximal deviation of kernel density estimates over general compact sets," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 230-241.
    6. Majid Mojirsheibani & William Pouliot, 2017. "Weighted bootstrapped kernel density estimators in two-sample problems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 61-84, January.
    7. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.

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