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Estimation in an Additive Model when the Components are LinkedParametrically

Carroll, Raymond J. ; Härdle, Wolfgang ; Mammen, Enno

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Abstract

Motivated by a nonparametric GARCH model we considernonparametric additive regression and autoregression modelsin the special case that the additive components are linked parametrically. We show that the parameter can be estimated with parametric rate and give the normal limit. Our procedure is based on two steps. In the first stepnonparametric smoothers are used for the estimation of each additivecomponent without taking into account the parametric link of thefunctions. In a second step the parameter is estimated by using theparametric restriction between the additive components. Interestingly, our method needs no undersmoothing in the first step.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 01 Jun 2016 12:46
Date: October 1998
Number of Pages: 30
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Controlled Keywords: GARCH-Prozess
Uncontrolled Keywords: Additive Models; Asymptotics; Autoregression; Finance; GARCH Models; Measurement Error; Nonparametric Regression; Time Series
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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