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

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  • Giordano, Francesco
  • Parrella, Maria Lucia

Abstract

The local polynomial estimator is particularly affected by the curse of dimensionality, which reduces the potential of this tool for large-dimensional applications. We propose an estimation procedure based on the local linear estimator and a sparseness condition that focuses on nonlinearities in the model. Our procedure, called BID (bias inflation–deflation), is automatic and easily applicable to models with many covariates without requiring any additivity assumption. It is an extension of the RODEO method, and introduces important new contributions: consistent estimation of the multivariate optimal bandwidth (the tuning parameter of the estimator); consistent estimation of the multivariate bias-corrected regression function and confidence bands; and automatic identification and separation of nonlinear and linear effects. Some theoretical properties of the method are discussed. In particular, we show the nonparametric oracle property. For linear models, BID automatically reaches the optimal rate Op(n−1/2), equivalent to the parametric case. A simulation study shows the performance of the procedure for finite samples.

Suggested Citation

  • Giordano, Francesco & Parrella, Maria Lucia, 2016. "Bias-corrected inference for multivariate nonparametric regression: Model selection and oracle property," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 71-93.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:71-93
    DOI: 10.1016/j.jmva.2015.08.016
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    Cited by:

    1. Alessandra Amendola & Francesco Giordano & Maria Lucia Parrella & Marialuisa Restaino, 2017. "Variable selection in high‐dimensional regression: a nonparametric procedure for business failure prediction," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(4), pages 355-368, August.

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