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Additive Regression Splines With Irrelevant Categorical and Continuous Regressors


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  • Shujie Ma
  • Jeffrey S. Racine


We consider the problem of estimating a relationship using semiparametric additive regression splines when there exist both continuous and categorical regressors, some of which are irrelevant but this is not known a priori. We show that choosing the spline degree, number of subintervals, and bandwidths via cross-validation can automatically remove irrelevant regressors, thereby delivering 'automatic dimension reduction' without the need for pre-testing. Theoretical underpinnings are provided, finite-sample performance is studied, and an illustrative application demonstrates the ecacy of the proposed approach in finite-sample settings. An R package implementing the methods is available from the Comprehensive R Archive Network (Racine and Nie (2011)).

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Bibliographic Info

Paper provided by McMaster University in its series Department of Economics Working Papers with number 2012-07.

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Length: 37 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:mcm:deptwp:2012-07

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Keywords: B-spline; discrete; kernel;

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  1. Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2012. "Spline Regression in the Presence of Categorical Predictors," Department of Economics Working Papers, McMaster University 2012-06, McMaster University.
  2. 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.
  3. Raymond J. Carroll & Arnab Maity & Enno Mammen & Kyusang Yu, 2009. "Nonparametric additive regression for repeatedly measured data," Biometrika, Biometrika Trust, Biometrika Trust, vol. 96(2), pages 383-398.
  4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, Princeton University Press, edition 1, volume 1, number 8355.
  5. QI Li & Desheng Ouyang & Jeffrey S. Racine, 2013. "Categorical semiparametric varying‐coefficient models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 28(4), pages 551-579, 06.
  6. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
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Cited by:
  1. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2013. "Bayesian bandwidth selection for a nonparametric regession model with mixed types of regressors," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 13/13, Monash University, Department of Econometrics and Business Statistics.
  2. Nicholas M. Kiefer & Jeffrey S. Racine, 2013. "The Smooth Colonel and the Reverend Find Common Ground," Department of Economics Working Papers, McMaster University 2013-03, McMaster University.
  3. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers, McMaster University 2012-08, McMaster University.
  4. Jean-Thomas Bernard & Michael Gavin & Lynda Khalaf & Marcel Voia, 2011. "The Environmental Kuznets Curve: Tipping Points, Uncertainty and Weak Identification," Cahiers de recherche CREATE, CREATE 2011-4, CREATE.


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