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Relative Efficiency with Equivalence Classes of Asymptotic Covariances


  • David M. Mandy

    (University of Missouri-Columbia)

  • Carlos Martins-Filho

    (Oregon State University)


White's (1984) concept of asymptotic variance is shown to allow some ambiguities when used to study asymptotic efficiency. These ambiguities are resolved with some mild conditions on the estimators being studied, because then White's asymptotic variance is an equivalence class in which efficiency conclusions are invariant across members of the class. Among the extant efficiency definitions, the liminf-based definition (White 1994, p. 136) is most informative even though identical conclusions can be obtained under our conditions with earlier definitions, but there are still some notions of efficiency allowed by White's asymptotic variance that can only be detected by weaker efficiency definitions.

Suggested Citation

  • David M. Mandy & Carlos Martins-Filho, 1998. "Relative Efficiency with Equivalence Classes of Asymptotic Covariances," Econometrics 9805001, EconWPA.
  • Handle: RePEc:wpa:wuwpem:9805001
    Note: 19 pages (title page, 18 numbered pages, 5 page appendix, references), Tex .dvi file

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    References listed on IDEAS

    1. White, Halbert, 1982. "Instrumental Variables Regression with Independent Observations," Econometrica, Econometric Society, vol. 50(2), pages 483-499, March.
    2. Bates, Charles E. & White, Halbert, 1993. "Determination of Estimators with Minimum Asymptotic Covariance Matrices," Econometric Theory, Cambridge University Press, vol. 9(04), pages 633-648, August.
    3. repec:cup:etheor:v:9:y:1993:i:4:p:633-48 is not listed on IDEAS
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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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