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Bootstrap estimation of the asymptotic variances of statistical functionals

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Abstract

A modified bootstrap estimator of the asymptotic variance of a statistical functional is studied. The modified bootstrap variance estimator circumvents the problem of the original bootstrap when the population distribution has heavy tails, and requires less stringent conditions for its consistency than the ordinary bootstrap variance estimator. The consistency of the modified bootstrap variance estimator is established for differentiable statistical functionals.

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References

  • Bickel, P. J. and Freedman, D. A. (1981). Some asymptotic theory for the bootstrap,Ann. Statist.,9, 1196–1217.

    MATH  MathSciNet  Google Scholar 

  • Efron, B. (1979). Bootstrap methods: Another look at the jackknife,Ann. Statist.,7, 1–26.

    MATH  MathSciNet  Google Scholar 

  • Efron, B. (1987). Better bootstrap confidence intervals,J. Amer. Statist. Assoc.,82, 171–200.

    Article  MATH  MathSciNet  Google Scholar 

  • Ghosh, M., Parr, W. C., Singh, K. and Babu, G. J. (1984). A note on bootstrapping the sample median,Ann. Statist.,12, 1130–1135.

    MATH  MathSciNet  Google Scholar 

  • Gill, R. D. (1989). Non- and semi-parametric maximum likelihood estimators and the von Mises method (Part I),Scand. J. Statist.,16, 97–128.

    MATH  MathSciNet  Google Scholar 

  • Hampel, F. R. (1974). The influence curve and its role in robust estimation,J. Amer. Statist. Assoc.,69, 383–397.

    Article  MATH  MathSciNet  Google Scholar 

  • Parr, W. C. (1985). Jackknifing differentiable statistical functionals,J. Roy. Statist. Soc. Ser. B,47, 56–66.

    MATH  MathSciNet  Google Scholar 

  • Rao, J. N. K. and Wu, C. F. J. (1988). Resampling inference with complex survey data,J. Amer. Statist. Assoc.,83, 231–241.

    Article  MATH  MathSciNet  Google Scholar 

  • Serfling, R. J. (1980).Approximation Theorems of Mathematical Statistics, Wiley, New York.

    MATH  Google Scholar 

  • Shao, J. (1988a). A note on bootstrap variance estimation, Tech. Report, Dept. of Statistics, Purdue University.

  • Shao, J. (1988b). Consistency of jackknife estimators of the variances of sample quantiles,Comm. Statist. A—Theory Methods,17, 3017–3028.

    MATH  Google Scholar 

  • Singh, K. (1981). On the asymptotic accuracy of Efron's bootstrap,Ann. Statist.,9, 1187–1195.

    MATH  MathSciNet  Google Scholar 

  • Swanepoel, J. W. H. (1986). A note on proving that the (modified) bootstrap works,Comm. Statist. A—Theory Methods,15, 3193–3203.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, K1N 6N5, Ottawa, Ontario, Canada

    Jun Shao

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  1. Jun Shao
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Shao, J. Bootstrap estimation of the asymptotic variances of statistical functionals. Ann Inst Stat Math 42, 737–752 (1990). https://doi.org/10.1007/BF02481147

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  • DOI: https://doi.org/10.1007/BF02481147

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