The Annals of Statistics

Functional Jackknifing: Rationality and General Asymptotics

Pranab Kumar Sen

Full-text: Open access

Abstract

Though jackknifing serves well the dual purpose of bias reduction and variance estimation, the pseudovariables it generates may not generally preserve robustness for general statistical functionals. These pseudovariables are incorporated in a differentiable functional detour of jackknifing, and along with its rationality, the related asymptotic theory is studied systematically. A two-step jackknifing is considered for the variance estimation. Second-order asymptotic distributional representations for the classical jackknifed estimators are also considered.

Article information

Source
Ann. Statist., Volume 16, Number 1 (1988), 450-469.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350714

Digital Object Identifier
doi:10.1214/aos/1176350714

Mathematical Reviews number (MathSciNet)
MR924880

Zentralblatt MATH identifier
0665.62030

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory 62F12: Asymptotic properties of estimators

Keywords
Asymptotic normality asymptotic variance bias bootstrap Frechet differentiability Hadamard derivative jackknifed variance perturbations pseudovariables robustness second-order representation statistical functional two-step jackknifing

Citation

Sen, Pranab Kumar. Functional Jackknifing: Rationality and General Asymptotics. Ann. Statist. 16 (1988), no. 1, 450--469. doi:10.1214/aos/1176350714. https://projecteuclid.org/euclid.aos/1176350714


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