The Annals of Statistics

Some Invariance Principles Relating to Jackknifing and Their Role in Sequential Analysis

Pranab Kumar Sen

Full-text: Open access

Abstract

For a broad class of jackknife statistics, it is shown that the Tukey estimator of the variance converges almost surely to its population counterpart. Moreover, the usual invariance principles (relating to the Wiener process approximations) usually filter through jackknifing under no extra regularity conditions. These results are then incorporated in providing a bounded-length (sequential) confidence interval and a preassigned-strength sequential test for a suitable parameter based on jackknife estimators.

Article information

Source
Ann. Statist., Volume 5, Number 2 (1977), 316-329.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343797

Digital Object Identifier
doi:10.1214/aos/1176343797

Mathematical Reviews number (MathSciNet)
MR443175

Zentralblatt MATH identifier
0365.62082

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 62E20: Asymptotic distribution theory 62G35: Robustness 62L10: Sequential analysis

Keywords
Almost sure convergence Brownian motions bounded-length confidence intervals invariance principles preassigned strength sequential tests jackknife stopping time tightness Tukey estimator of the variance $U$-statistics von Misses' functionals

Citation

Sen, Pranab Kumar. Some Invariance Principles Relating to Jackknifing and Their Role in Sequential Analysis. Ann. Statist. 5 (1977), no. 2, 316--329. doi:10.1214/aos/1176343797. https://projecteuclid.org/euclid.aos/1176343797


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