Asymptotic behaviour of estimation equations with functional nuisance or working parameter

Pruscha, H. und Wellisch, U. (1997): Asymptotic behaviour of estimation equations with functional nuisance or working parameter. Sonderforschungsbereich 386, Discussion Paper 79

Abstract

We are concerned with the asymptotic theory of semiparametric estimation equations. We are dealing with estimation equations which have a parametric component of interest and a functional (nonparametric) nuisance component. We give sufficient conditions for the existence and the asymptotic normality of a consistent estimation equation estimator for the parameter of interest. These conditions concern the asymptotic distribution of the estimation function and of its derivative as well as the effect of the functional nuisance part in the estimation equation. In order to treat the nonparametric component we introduce a general differential calculus and a general mean value theorem. For the nonparametric part in the estimation equation we distinguish two cases: the situation of a (classical) nuisance parameter and the case of a so called working parameter. As a special case we get regularity conditions for estimation equations with finite dimensional nuisance or working parameter. As an example we present the semiparametric linear regression model.

• Dokumententyp: Paper
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch