Perturbation invariant estimates and incidental nuisance parameters

Publication: Working/Discussion PaperWU Working Paper


It is shown (Proposition (3.9)) that the asymptotic information bound which is valid for the estimation of a parameter in the structure (mixture) model remains valid in the functional model (incidental nuisance parameters) if only perturbation symmetric estimators (Definition (3.6)) are admitted. Pertur- bation symmetry is a property which is closely related to permutation symmetry (Theorem (3.4)). In particular, equicontinuous functions of empirical processes are perturbation symmetric (Theorem (3.3)). Thus, the results of this paper continue a discussion initiated by Bickel and Klaassen (1986), Pfanzagl (1993) and Strasser (1996) on permutation symmetry of estimators and the exclusion of superefficiency in the functional model. (authors' abstract)
Original languageEnglish
Place of PublicationVienna
PublisherInstitut für Statistik und Mathematik, WU Vienna University of Economics and Business
Publication statusPublished - 1996

Publication series

NameForschungsberichte / Institut für Statistik

WU Working Paper Series

  • Forschungsberichte / Institut für Statistik

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