Optimal smoothing for a computationally and statistically efficient single index estimator - Yingcun Xia; Wolfgang Karl Härdle; Oliver Linton (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2009)
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.
Keywords: C00; C13; C14; 330; ADE; Asymptotics; Bandwidth; MAVE method; Semi-parametric efficiency; Schätztheorie; Nichtparametrisches Verfahren; Theorie