Inference for the Direction of the Larger of Two Eigenvectors: The Case of Circular Elongation

  • Stephan Morgenthaler
  • John W. Tukey
Part of the Lecture Notes in Statistics book series (LNS, volume 109)


The paper discusses interval estimation of the dominant eigenvector for two-dimensional data. We derive adjustments for both the classical asymptotic formula of Anderson (1963) and two jackknife estimators and exhibit the finite sample behavior of the resulting interval (wedge) estimators in a variety of situations, including nonGaussian and non-circular parent distributions.

Key words and phrases

Interval estimation eigendirections jackknife finite sample adjustments bivariate nonGaussian bivariate distributions nonelliptical bivariate distributions cross-t circ-t exx-t 

AMS subject classifications

62H25 62H10 62G35 


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  1. [1]
    Anderson, T.W. (1963): Asymptotic theory for principal component analysis. Ann. Math. Statist. 34 122–148.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Quenouille, M. (1956): Notes on bias in estimation. Biometrika 43 353–360.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Tukey, J.W. (1958): Bias and confidence in not quite large samples (abstract). Ann. Math. Statist. 29 614.CrossRefGoogle Scholar
  4. [4]
    Tukey, J.W. (1993): Major challenges for multiple-response (and multiple-adjustment) analysis. In Multivariate Analysis: Future Directions (C.R. Rao, ed.), p. 401–421. North Holland, Amsterdam.Google Scholar
  5. [5]
    Tyler, D.E. (1981): Asymptotic inference for eigenvectors. Ann. Statist. 9 725–736.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Wu, C.F.J. (1985): Statistical Methods Based on Data Resampling. Special invited paper presented at IMS Meeting in Stony Brook.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Stephan Morgenthaler
    • 1
  • John W. Tukey
    • 2
  1. 1.ETH LausanneSwitzerland
  2. 2.Princeton UniversityNew JerseyUSA

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