Skip to main content
SpringerLink
Log in

Asymptotically Efficient Importance Sampling for Bootstrap

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

The Large Deviation Principle is proved for the conditional probabilities of moderate deviations of weighted empirical bootstrap measures with respect to a fixed empirical measure. Using this LDP for the problem of calculation of moderate deviation probabilities of differentiable statistical functionals, it is shown that the importance sampling based on influence function is asymptotically efficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. A. Bucklew, Large Deviations Techniques in Decision, Simulation and Estimation, Wiley, New York (1990).

    Google Scholar 

  2. J. A. Bucklew, P. Ney, and J. S. Sadowsky, “Monte-Carlo simulation and large deviation theory for uniformly recurrent Markov chains,” J. Appl. Probab., 27, 44–59 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  3. M. S. Ermakov, “Importance sampling for simulation of moderate deviation probabilities of statistics,” Stat. Decision, 25, 265–284 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. S. Ermakov, “Large deviation principle for moderate deviation probabilities of empirical bootstrap measures,” Zap. Nauchn. Semin. POMI, 412, 135–177 (2013).

    Google Scholar 

  5. F. Gao and X. Zhao, “Delta method in large deviations and moderate deviations for estimators,” Ann. Statist., 39, 1211–1240 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Johns, “Importance sampling for bootstrap confidence intervals,” J. Amer. Statist. Assoc., 83(403), 709–714 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag, New York (1975).

    Book  MATH  Google Scholar 

  8. J. S. Sadowsky, “On Monte-Carlo estimation of large deviation probabilities,” Ann. Appl. Probab., 6, 399–422 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  9. J. S. Sadowsky and J. A. Bucklew, “On large deviation theory and asymptotically efficient Monte-Carlo estimation,” IEEE Trans. Inf. Theory, 36, 579–588 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Saulis and V. Statuliavichius, Limit Theorems for Large Deviations [in Russian], Mokslas, Vilnius (1989).

    Google Scholar 

  11. A. W. van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes With Applications to Statistics, Springer, New York (1996).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanical Engineering Problems RAS, St.Petersburg, Russia

    M. S. Ermakov

Authors
  1. M. S. Ermakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. S. Ermakov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 431, 2014, pp. 82–96.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ermakov, M.S. Asymptotically Efficient Importance Sampling for Bootstrap. J Math Sci 214, 474–483 (2016). https://doi.org/10.1007/s10958-016-2791-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-2791-4

Keywords

Search

Navigation