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On a modified bootstrap for certain asymptotically nonnormal statistics

Author

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  • Datta, Somnath

Abstract

The classical bootstrap approximation is known to break down (Babu, 1984), even for "nice" statistics such as a smooth function of a multivariate sample mean for certain "critical" values of the mean vector. A simple modification of the naive bootstrap is suggested to take care of this problem. Simulation results show improvements at or near a critical value while using the modified bootstrap. Asymptotic validity (with rate of convergence) of the modified bootstrap is established for parameter values including the critical values.

Suggested Citation

  • Datta, Somnath, 1995. "On a modified bootstrap for certain asymptotically nonnormal statistics," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 91-98, August.
  • Handle: RePEc:eee:stapro:v:24:y:1995:i:2:p:91-98
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    References listed on IDEAS

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    1. Kanazawa, Yuichiro, 1993. "Hellinger distance and Kullback--Leibler loss for the kernel density estimator," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 315-321, November.
    2. Kanazawa, Yuichiro, 1993. "Hellinger distance and Akaike's information criterion for the histogram," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 293-298, July.
    3. Hall, Peter, 1983. "On near neighbour estimates of a multivariate density," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 24-39, March.
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    Cited by:

    1. Hoderlein, Stefan & Winter, Joachim, 2010. "Structural measurement errors in nonseparable models," Journal of Econometrics, Elsevier, pages 432-440.
    2. Camponovo, Lorenzo & Scaillet, Olivier & Trojani, Fabio, 2012. "Robust subsampling," Journal of Econometrics, Elsevier, vol. 167(1), pages 197-210.
    3. Chang, Christopher C. & Politis, Dimitris N., 2011. "Bootstrap with larger resample size for root-n consistent density estimation with time series data," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 652-661, June.

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