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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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    1. La Rocca, Michele & Perna, Cira, 2005. "Variable selection in neural network regression models with dependent data: a subsampling approach," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 415-429, February.
    2. Lu, Zhan-Qian, 1996. "Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 187-205, November.
    3. Ying Dai & Shuangge Ma, 2012. "Variable selection for semiparametric regression models with iterated penalisation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 283-298.
    4. Radchenko, Peter & James, Gareth M., 2010. "Variable Selection Using Adaptive Nonlinear Interaction Structures in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1541-1553.
    5. L. Yang & R. Tschernig, 1999. "Multivariate bandwidth selection for local linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 793-815.
    6. Lu Lin & Feng Li, 2008. "Stable and bias-corrected estimation for nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 283-303.
    7. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    8. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
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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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