Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/39295 
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dc.contributor.authorCui, Xiaen
dc.contributor.authorHärdle, Wolfgang Karlen
dc.contributor.authorZhu, Lixingen
dc.date.accessioned2009-11-05-
dc.date.accessioned2010-08-26T11:56:51Z-
dc.date.available2010-08-26T11:56:51Z-
dc.date.issued2009-
dc.identifier.urihttp://hdl.handle.net/10419/39295-
dc.description.abstractGeneralized single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and financial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, beta = 1, represents a non-regular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM approach, a method of estimating functions, to study the generalized single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the resulting estimating equations is achieved, and a Wilk's type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. (1997). A fixed point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement.en
dc.language.isoengen
dc.publisher|aHumboldt University of Berlin, Collaborative Research Center 649 - Economic Risk |cBerlinen
dc.relation.ispartofseries|aSFB 649 Discussion Paper |x2009,050en
dc.subject.jelC02en
dc.subject.jelC13en
dc.subject.jelC14en
dc.subject.jelC21en
dc.subject.ddc330en
dc.subject.keywordGeneralized single-index modelen
dc.subject.keywordindex coefficientsen
dc.subject.keywordestimating equationsen
dc.subject.keywordasymptotic propertiesen
dc.subject.keyworditerationen
dc.subject.stwSchätztheorieen
dc.subject.stwNichtparametrisches Verfahrenen
dc.subject.stwTheorieen
dc.titleGeneralized single-index models: The EFM approach-
dc.type|aWorking Paperen
dc.identifier.ppn612287130en
dc.rightshttp://www.econstor.eu/dspace/Nutzungsbedingungenen

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