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dc.contributor.authorGiordano, Francesco
dc.contributor.authorParrella, Maria Lucia
dc.date.accessioned2016-07-14T09:49:54Z
dc.date.available2016-07-14T09:49:54Z
dc.date.issued2014
dc.identifier.citationGiordano, F. and Parrella, M. L. (2014). “Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property”. DISES Working Paper 3.232, Università degli Studi di Salerno, Dipartimento di Scienze Economiche e Statistiche.it_IT
dc.identifier.issn1971-3029it_IT
dc.identifier.urihttp://hdl.handle.net/10556/2128
dc.description.abstractThe local polynomial estimator is particularly affected by the curse of di- mensionality. So, the potentialities of such a tool become ineffective for large dimensional applications. Motivated by this, we propose a new estimation procedure based on the local linear estimator and a nonlinearity sparseness condition, which focuses on the number of covariates for which the gradient is not constant. Our procedure, called BID for Bias-Inflation-Deflation, is automatic and easily applicable to models with many covariates without any additive assumption to the model. It simultaneously gives a consistent estimation of a) the optimal bandwidth matrix, b) the multivariate regression function and c) the multivariate, bias-corrected, confidence bands. Moreover, it automatically identify the relevant covariates and it separates the nonlinear from the linear effects. We do not need pilot bandwidths. Some theoretical properties of the method are discussed in the paper. In particular, we show the nonparametric oracle property. For linear models, the BID automatically reaches the optimal rate Op(n−1/2), equivalent to the parametric case. A simulation study shows a good performance of the BID procedure, compared with its direct competitor.it_IT
dc.format.extent26 p.it_IT
dc.language.isoenit_IT
dc.relation.ispartofWorking Papers ; 3.232it_IT
dc.sourceUniSa. Sistema Bibliotecario di Ateneoit_IT
dc.subjectMultivariate nonparametric regressionit_IT
dc.subjectMultivariate bandwidth selectionit_IT
dc.subjectMultivariate confidence bandsit_IT
dc.titleBias-corrected inference for multivariate nonparametric regression: model selection and oracle propertyit_IT
dc.typeWorking Paperit_IT
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