The Annals of Mathematical Statistics

On the Jackknife Statistic, Its Extensions, and Its Relation to $e_n$- Transformations

H. L. Gray, T. A. Watkins, and J. E. Adams

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Abstract

In this paper, a complete overview is given of the theoretical development of various estimators generated by the jackknife statistic. In particular, the jackknife method is extended to stochastic processes by means of two estimators referred to as the $J_\infty$-estimator and the $J_\infty^{(2)}$-estimator. These estimators are studied in some detail and shown to have the same properties as the jackknife when one considers the length of the process record as the sample size. Finally, it is shown that the entire development of the jackknife procedures discussed in this paper can be considered as a direct parallel of earlier developments in numerical analysis surrounding the study of a transformation referred to as the $e_n$-transformation.

Article information

Source
Ann. Math. Statist., Volume 43, Number 1 (1972), 1-30.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692697

Digital Object Identifier
doi:10.1214/aoms/1177692697

Mathematical Reviews number (MathSciNet)
MR303642

Zentralblatt MATH identifier
0262.62014

JSTOR
links.jstor.org

Citation

Gray, H. L.; Watkins, T. A.; Adams, J. E. On the Jackknife Statistic, Its Extensions, and Its Relation to $e_n$- Transformations. Ann. Math. Statist. 43 (1972), no. 1, 1--30. doi:10.1214/aoms/1177692697. https://projecteuclid.org/euclid.aoms/1177692697


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