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Sparse regularized local regression

Author

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  • Vidaurre, Diego
  • Bielza, Concha
  • Larrañaga, Pedro

Abstract

The intention is to provide a Bayesian formulation of regularized local linear regression, combined with techniques for optimal bandwidth selection. This approach arises from the idea that only those covariates that are found to be relevant for the regression function should be considered by the kernel function used to define the neighborhood of the point of interest. However, the regression function itself depends on the kernel function. A maximum posterior joint estimation of the regression parameters is given. Also, an alternative algorithm based on sampling techniques is developed for finding both the regression parameter distribution and the predictive distribution.

Suggested Citation

  • Vidaurre, Diego & Bielza, Concha & Larrañaga, Pedro, 2013. "Sparse regularized local regression," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 122-135.
    • Handle: RePEc:eee:csdana:v:62:y:2013:i:c:p:122-135
    DOI: 10.1016/j.csda.2013.01.008
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    References listed on IDEAS

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    1. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    2. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2012. "Lazy lasso for local regression," Computational Statistics, Springer, vol. 27(3), pages 531-550, September.
    3. 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.
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    Cited by:

    1. Gaure, Simen, 2013. "OLS with multiple high dimensional category variables," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 8-18.

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