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Perturbation invariant estimates and incidental nuisance parameters

Strasser, Helmut (1996) Perturbation invariant estimates and incidental nuisance parameters. Forschungsberichte / Institut für Statistik, 48. Institut für Statistik und Mathematik, WU Vienna University of Economics and Business, Vienna.

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Abstract

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)

Item Type: Paper
Additional Information: published as: Helmut Strasser (1998), Perturbation Invariant Estimates and Incidental Nuisance Parameters, Mathematical Methods of Statistics, 7, 1-26.
Keywords: Störungstheorie
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 09 Jun 2004 19:36
Last Modified: 13 Jan 2017 11:09
URI: http://epub.wu.ac.at/id/eprint/1138

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