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Estimation In An Additive Model When The Components Are Linked Parametrically

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Author Info

  • Carroll, Raymond J.
  • H rdle, Wolfgang
  • Mammen, Enno

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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 04 (August)
Pages: 886-912

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Handle: RePEc:cup:etheor:v:18:y:2002:i:04:p:886-912_18

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Cited by:
  1. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Yang, Lijian, 2006. "A semiparametric GARCH model for foreign exchange volatility," Journal of Econometrics, Elsevier, vol. 130(2), pages 365-384, February.
  3. Dette, Holger & Pardo-Fernandez, Juan Carlos & van Keilegom, Ingrid, 2007. "Goodness-of-fit tests for multiplicativemodels with dependent data," Technical Reports 2007,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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