The Annals of Statistics

Applications of Anova Type Decompositions for Comparisons of Conditional Variance Statistics Including Jackknife Estimates

Samuel Karlin and Yosef Rinott

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Abstract

Variance and bias comparisons are set forth for a sequence of nonlinear statistics based on independent random variables including jackknife and U-statistics of various orders. The analysis relies heavily on an orthogonal decomposition first introduced by Hoeffding in 1948. This ANOVA type decomposition is refined for purposes of discerning higher order convexity properties for an array of conditional variance coefficients. There is also some discussion of two-sample statistics.

Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 485-501.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345790

Digital Object Identifier
doi:10.1214/aos/1176345790

Mathematical Reviews number (MathSciNet)
MR653524

Zentralblatt MATH identifier
0491.62036

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation

Keywords
Orthogonal decomposition jackknife statistics bias comparisons absolute monotonicity

Citation

Karlin, Samuel; Rinott, Yosef. Applications of Anova Type Decompositions for Comparisons of Conditional Variance Statistics Including Jackknife Estimates. Ann. Statist. 10 (1982), no. 2, 485--501. doi:10.1214/aos/1176345790. https://projecteuclid.org/euclid.aos/1176345790


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