Estimation in an additive model when the components are linked parametrically - Raymond J. Carroll; Wolfgang Härdle; Enno Mammen (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 1999)
Motivated by a nonparametric GARCH model we consider nonparametric additive regression and 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.
urn:nbn:de:kobv:11-10055992
Keywords: 330; Finance; Nonparametric Regression; Additive Models; Asymptotics; Autoregression; GARCH Models; Measurement Error; Time Series