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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Francesco Giordano & Maria Lucia Parrella, 2014. "Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property," Working Papers 3_232, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
  • Handle: RePEc:sep:wpaper:3_232
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    multivariate nonparametric regression; multivariate bandwidth selection; multivariate confidence bands.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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