Flexible Generalized Varying Coefficient Regressions Models

Lee, Young K. ; Mammen, Enno ; Park, Byeong U.

DOI: https://doi.org/10.1214/12-AOS1026
URL: http://arxiv.org/pdf/1210.4711.pdf
Additional URL: http://projecteuclid.org/euclid.aos/1350394521
Document Type: Article
Year of publication: 2012
The title of a journal, publication series: The Annals of Statistics
Volume: 40
Issue number: 3
Page range: 1906-1933
Place of publication: Cleveland, Ohio [u.a.]
Publishing house: Inst. of Mathematical Statistics
ISSN: 0090-5364
Publication language: English
Institution: School of Law and Economics > Statistik (Mammen)
Außerfakultäre Einrichtungen > SFB 884
Subject: 510 Mathematics
Keywords (English): Varying coefficient models , kernel smoothing , entropy projection , Hilbert space , quasi-likelihood integral equation , Newton–Raphson approximation
Abstract: In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial estimators of the coefficient functions onto a Hilbert space with a suitable norm. We provide a backfitting algorithm to compute the estimators. We show that the algorithm converges at a geometric rate under weak conditions. We derive the asymptotic distributions of the estimators and show that the estimators have the oracle properties. This is done for the general order of local polynomial fitting and for the estimation of the derivatives of the coefficient functions, as well as the coefficient functions themselves. The estimators turn out to have several theoretical and numerical advantages over the marginal integration estimators studied by Yang, Park, Xue and Härdle [J. Amer. Statist. Assoc. 101 (2006) 1212–1227].

Dieser Eintrag ist Teil der Universitätsbibliographie.

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