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Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints

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  • Pang Du
  • Christopher F. Parmeter
  • Jeffrey S. Racine

Abstract

Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression method in Hall and Huang (2001) to the multivariate and multi-constraint setting. We impose equality and/or inequality constraints on a nonparametric kernel regression model and its derivatives. A bootstrap procedure is also proposed for testing the validity of the constraints. Consistency of our constrained kernel estimator is provided through an asymptotic analysis of its relationship with the unconstrained estimator. Theoretical underpinnings for the bootstrap procedure are also provided. Illustrative Monte Carlo results are presented and an application is considered.

Suggested Citation

  • 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.
    • Handle: RePEc:mcm:deptwp:2012-08
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    11. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.
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    Keywords

    shape restrictions; nonparametric regression; multivariate kernel estimation; hypothesis testing;
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