@techreport{Xia2009Optimal,
abstract = {In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothing may result as we show from inefficient estimation methods or technical difficulties. Based on local linear kernel smoother, we propose an estimation method to estimate the single-index model without under-smoothing. Under some conditions, our estimator of the single-index is asymptotically normal and most efficient in the semi-parametric sense. Moreover, we derive higher expansions for our estimator and use them to define an optimal bandwidth for the purposes of index estimation. As a result we obtain a practically more relevant method and we show its superior performance in a variety of applications.},
address = {Berlin},
author = {Yingcun Xia and Wolfgang Karl H\"{a}rdle and Oliver Linton},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C00; C13; C14; 330; ADE; Asymptotics; Bandwidth; MAVE method; Semi-parametric efficiency; Sch\"{a}tztheorie; Nichtparametrisches Verfahren; Theorie},
language = {eng},
number = {2009,028},
publisher = {SFB 649, Economic Risk},
title = {Optimal smoothing for a computationally and statistically efficient single index estimator},
type = {SFB 649 discussion paper},
url = {http://hdl.handle.net/10419/25344},
year = {2009}
}
