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Additive Regression Splines With Irrelevant Categorical and Continuous Regressors

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  • Shujie Ma
  • Jeffrey S. Racine

Abstract

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 efficacy 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)).

Suggested Citation

  • Shujie Ma & Jeffrey S. Racine, 2012. "Additive Regression Splines With Irrelevant Categorical and Continuous Regressors," Department of Economics Working Papers 2012-07, McMaster University.
    • Handle: RePEc:mcm:deptwp:2012-07
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    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2012-07.pdf
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    References listed on IDEAS

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    1. QI Li & Desheng Ouyang & Jeffrey S. Racine, 2013. "Categorical semiparametric varying‐coefficient models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 551-579, June.
    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. Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2015. "Spline Regression in the Presence of Categorical Predictors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 705-717, August.
    4. Raymond J. Carroll & Arnab Maity & Enno Mammen & Kyusang Yu, 2009. "Nonparametric additive regression for repeatedly measured data," Biometrika, Biometrika Trust, vol. 96(2), pages 383-398.
    5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    6. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
    7. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
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    Cited by:

    1. Paudel, Krishna P. & Lin, C.-Y. Cynthia & Pandit, Mahesh, 2014. "Environmental Kuznets Curve for Water Quality Parameters at Global Level," 2014 Annual Meeting, February 1-4, 2014, Dallas, Texas 162618, Southern Agricultural Economics Association.
    2. Jean-Thomas Bernard & Michael Gavin & Lynda Khalaf & Marcel Voia, 2015. "Environmental Kuznets Curve: Tipping Points, Uncertainty and Weak Identification," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(2), pages 285-315, February.
    3. Pandit, Mahesh & Paudel, Krishna P. & Williams, Deborah, 2014. "Effect of Remittance on Intensity of Agricultural Technology Adoption in Nepal," 2014 Annual Meeting, February 1-4, 2014, Dallas, Texas 162692, Southern Agricultural Economics Association.
    4. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    5. Ferris, J. Stephen & Voia, Marcel C., 2015. "The effect of federal government size on private economic performance in Canada: 1870–2011," Economic Modelling, Elsevier, vol. 49(C), pages 172-185.
    6. J. Stephen Ferris & Marcel-Cristian Voia, 2014. "Does Aggregate Government Size Effect Private Economic Performance in Canada?," Carleton Economic Papers 14-13, Carleton University, Department of Economics.
    7. Nicholas M. Kiefer & Jeffrey S. Racine, 2017. "The smooth colonel and the reverend find common ground," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 241-256, March.
    8. Lien, Donald & Hu, Yue & Liu, Long, 2017. "A note on using ratio variables in regression analysis," Economics Letters, Elsevier, vol. 150(C), pages 114-117.
    9. Geraldine Henningsen & Arne Henningsen & Christian Henning, 2015. "Transaction costs and social networks in productivity measurement," Empirical Economics, Springer, vol. 48(1), pages 493-515, February.
    10. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2016. "Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors," Econometrics, MDPI, vol. 4(2), pages 1-27, April.

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