Relative efficiency with equivalence classes of asymptotic covariances

摘要

White's (1984, Asymptotic Theory for Econometricians. Academic Press (Harcourt Brace Jovanovich), Orlando.) 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 lim inf-based definition (White, 1994. Estimation, Inference and Specification Analysis. Econometric Society Monograph, vol. 22, Cambridge University Press, Cambridge. 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.