Perturbation invariant estimates and incidental nuisance parameters

Publikation: 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)
HerausgeberInstitut für Statistik und Mathematik, WU Vienna University of Economics and Business
PublikationsstatusVeröffentlicht - 1996


NameForschungsberichte / Institut für Statistik

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