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On the bootstrap and the trimmed mean

Author

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  • Hall, Peter
  • Padmanabhan, A. R.

Abstract

We show that the bootstrap approximation to the distribution of the Studentized trimmed mean performs better than the normal approximation, in that it is in error by terms of smaller order than n-1/2, where n denotes sample size. No assumptions are made about symmetry and only mild smoothness conditions are imposed. The method of proof involves differential smoothing of the bootstrap approximant, and is applicable to important related problems such as bootstrap approximation of the distribution of the trimmed variance.

Suggested Citation

  • Hall, Peter & Padmanabhan, A. R., 1992. "On the bootstrap and the trimmed mean," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 132-153, April.
    • Handle: RePEc:eee:jmvana:v:41:y:1992:i:1:p:132-153
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    Cited by:

    1. Zhiqiang Chen & Evarist Giné, 2004. "Another approach to asymptotics and bootstrap of randomly trimmed means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 771-790, December.
    2. Rand Wilcox, 2001. "Pairwise comparisons of trimmed means for two or more groups," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 343-356, September.
    3. Zhihong Liu & Qi Zhang & Raouf Boutaba & Yaping Liu & Zhenghu Gong, 2016. "ROUTE: run‐time robust reducer workload estimation for MapReduce," International Journal of Network Management, John Wiley & Sons, vol. 26(3), pages 224-244, May.

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