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ESTIMATION IN AN ADDITIVE MODEL WHEN THE COMPONENTS ARE LINKED PARAMETRICALLY

Published online by Cambridge University Press:  17 May 2002

Raymond J. Carroll
Affiliation:
Texas A&M University
Wolfgang Härdle
Affiliation:
Humboldt-Universität zu Berlin
Enno Mammen
Affiliation:
Ruprecht-Karls-Universität Heidelberg

Abstract

Motivated by a nonparametric GARCH model we consider nonparametric additive autoregression models in 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 step nonparametric smoothers are used for the estimation of each additive component without taking into account the parametric link of the functions. In a second step the parameter is estimated by using the parametric restriction between the additive components. Interestingly, our method needs no undersmoothing in the first step.

Type
Research Article
Copyright
© 2002 Cambridge University Press

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