Spline Regression in the Presence of Categorical Predictors

Authors

  • Shujie Ma,

    1. Department of Statistics, University of California, Riverside, CA, USA
    2. Center for Advanced Statistics and Econometrics Research, Soochow University, Suzhou, China
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  • Jeffrey S. Racine,

    Corresponding author
    1. Department of Economics and Graduate Program in Statistics, McMaster University, Hamilton, Ontario, Canada
    2. School of Economics, La Trobe University, Melbourne, Victoria, Australia
    • Correspondence to: Jeffrey S. Racine, Department of Economics, Kenneth Taylor Hall, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M4, Canada. E-mail:racinej@mcmaster.ca

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  • Lijian Yang

    1. Center for Advanced Statistics and Econometrics Research, Soochow University, Suzhou, China
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Summary

We consider the problem of estimating a relationship nonparametrically using regression splines when there exist both continuous and categorical predictors. We combine the global properties of regression splines with the local properties of categorical kernel functions to handle the presence of categorical predictors rather than resorting to sample splitting as is typically done to accommodate their presence. The resulting estimator possesses substantially better finite-sample performance than either its frequency-based peer or cross-validated local linear kernel regression or even additive regression splines (when additivity does not hold). Theoretical underpinnings are provided and Monte Carlo simulations are undertaken to assess finite-sample behavior; and two illustrative applications are provided. An implementation in R is available; see the R package ‘crs’ for details. Copyright © 2014 John Wiley & Sons, Ltd.

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