Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property

Francesco Giordano () and Maria Lucia Parrella ()
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Francesco Giordano: Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno
Maria Lucia Parrella: Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno

No 3_232, Working Papers from Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno

Abstract: The local polynomial estimator is particularly affected by the curse of dimensionality. 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.

Keywords: multivariate nonparametric regression; multivariate bandwidth selection; multivariate confidence bands. (search for similar items in EconPapers)
JEL-codes: C14 C15 C18 C88 (search for similar items in EconPapers)
Date: 2014-09
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Published in Working Papers, September 2014, pages 1-26

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