title: Direct Estimation of Low Dimensional Components in Additive Models
creator: Fan, Jianqing
creator: Härdle, Wolfgang
creator: Mammen, Enno
subject: 310
subject: 310 General statistics
subject: 510
subject: 510 Mathematics
description: Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory. In this paper an asymptotic treatment of this estimate is offered for several models. A modification of this procedure is introduced. We consider weighted marginal integration for local linear fits and we show that this estimate has the following advantages.    (i) With an appropriate choice of the weight function, the additive components can be efficiently estimated: An additive component can be estimated with the same asymptotic bias and variance as if the other components were known.    (ii) Application of local linear fits reduces the design related bias.
publisher: IMS Business Office
date: 1998
type: Article
type: info:eu-repo/semantics/article
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/20870/1/beitrag.38.pdf
identifier: DOI:10.11588/heidok.00020870
identifier: urn:nbn:de:bsz:16-heidok-208702
identifier:   Fan, Jianqing ; Härdle, Wolfgang ; Mammen, Enno  (1998) Direct Estimation of Low Dimensional Components in Additive Models.  The annals of statistics, 26 (3).  pp. 943-971.  ISSN 0090-5364     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20870/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng