Skip to main content
SpringerLink
Log in

One-step jackknife for M-estimators computed using Newton's method

  • Estimation
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

To estimate the dispersion of an M-estimator computed using Newton's iterative method, the jackknife method usually requires to repeat the iterative process n times, where n is the sample size. To simplify the computation, one-step jackknife estimators, which require no iteration, are proposed in this paper. Asymptotic properties of the one-step jackknife estimators are obtained under some regularity conditions in the i.i.d. case and in a linear or nonlinear model. All the one-step jackknife estimators are shown to be asymptotically equivalent and they are also asymptotically equivalent to the original jackknife estimator. Hence one may use a dispersion estimator whose computation is the simplest. Finite sample properties of several one-step jackknife estimators are examined in a simulation study.

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

  • Brillinger, D. (1964). The asymptotic behavior of Tukey's general method of setting approximate confidence limits (the jackknife) when applied to maximum likelihood estimates, Rev. Int. Statist. Inst., 32, 202–206.

    Google Scholar 

  • Efron, B. (1982). The Jackknife, the Bootstrap, and Other Resampling Plans, SIAM, Philadelphia.

    Google Scholar 

  • Fox, T., Hinkley, D. and Larntz, K. (1980). Jackknifing in non-linear regression, Technometrics, 22, 29–33.

    Google Scholar 

  • Huber, P. J. (1981). Robust Statistics, Wiley, New York.

    Google Scholar 

  • Jorgensen, M. A. (1987). Jackknifing fixed points of iterations, Biometrika, 74, 207–211.

    Google Scholar 

  • Lehmann, E. L. (1983). Theory of Point Estimation, Wiley, New York.

    Google Scholar 

  • Miller, R. M. (1974). An unbalanced jackknife, Ann. Statist., 2, 880–891.

    Google Scholar 

  • Reeds, J. A. (1978). jackknifing maximum likelihood estimates, Ann. Statist., 6, 727–739.

    Google Scholar 

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

    Google Scholar 

  • Shao, J. and Wu, C. F. J. (1987). Heteroscedasticity-robustness of jackknife variance estimators in linear models, Ann. Statist., 15, 1563–1579.

    Google Scholar 

  • Tukey, J. (1958). Bias and confidence in not quite large samples, Ann. Math. Statist., 29, 614.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, Ontario, Canada

    Jun Shao

Authors
  1. Jun Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research was supported by Natural Sciences and Engineering Research Council of Canada.

About this article

Cite this article

Shao, J. One-step jackknife for M-estimators computed using Newton's method. Ann Inst Stat Math 44, 687–701 (1992). https://doi.org/10.1007/BF00053398

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00053398

Key words and phrases

Search

Navigation