期刊名称：GREQAM Documents de Travail / Groupement de Recherche en Economie Quantitative d'Aix-Marseille
出版年度：1998
摘要：A geometrical setting is constructed, based on Hilbert space, in which the asymptotic properties of estimators can be studied. Estimators are defined in the context of parametrised models, which are treated as submanifolds of an underlying Hilbert manifold, on which a parameter-defining mapping is defined as a submersion on to a finite-dimensional parameter space. Robustness of an estimator is defined as its root-$n$ consistency at all points in the model, and efficiency is based on the criterion, natural in the Hilbert space setting, of the asymptotic variance. Robustness and efficiency at a given data-generating process (DGP) are given geometrical characterisations in terms of a finite-dimensional subspace, associated with asymptotically efficient estimation, of the tangent space at that DGP. Starting from an arbitrary consistent estimator, it is shown how a one-step efficient estimator can be obtained by orthogonal projection on to the efficient subspace. Examples are given, based mostly on the linear regression model.
