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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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    3. 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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    6. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.
    7. Léopold Simar & Ingrid Keilegom & Valentin Zelenyuk, 2017. "Nonparametric least squares methods for stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 47(3), pages 189-204, June.
    8. Kelly D.T.Trinh & Valentin Zelenyuk, 2015. "Productivity Growth and Convergence: Revisiting Kumar and Russell (2002)," CEPA Working Papers Series WP112015, School of Economics, University of Queensland, Australia.
    9. Czekaj, Tomasz G., 2015. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," 2015 Conference, August 9-14, 2015, Milan, Italy 211555, International Association of Agricultural Economists.
    10. Mengistu Assefa Wendimu & Arne Henningsen & Tomasz Gerard Czekaj, 2017. "Incentives and moral hazard: plot level productivity of factory-operated and outgrower-operated sugarcane production in Ethiopia," Agricultural Economics, International Association of Agricultural Economists, vol. 48(5), pages 549-560, September.
    11. Christopher Parmeter & Kai Sun & Daniel Henderson & Subal Kumbhakar, 2014. "Estimation and inference under economic restrictions," Journal of Productivity Analysis, Springer, vol. 41(1), pages 111-129, February.
    12. Jeffrey S. Racine, 2016. "Local Polynomial Derivative Estimation: Analytic or Taylor?," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 617-633, Emerald Group Publishing Limited.
    13. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    14. Francesco Vidoli & Giancarlo Ferrara, 2015. "Analyzing Italian citrus sector by semi-nonparametric frontier efficiency models," Empirical Economics, Springer, vol. 49(2), pages 641-658, September.
    15. Humberto Brea-Solis & Sergio Perelman & David Saal, 2017. "Regulatory incentives to water losses reduction: the case of England and Wales," Journal of Productivity Analysis, Springer, vol. 47(3), pages 259-276, June.
    16. Wenchuan Liu & Yu Zhang & Qi Li, 2015. "A semiparametric varying coefficient model of monotone auction bidding processes," Empirical Economics, Springer, vol. 48(1), pages 313-335, February.
    17. Kai Sun, 2015. "Constrained nonparametric estimation of input distance function," Journal of Productivity Analysis, Springer, vol. 43(1), pages 85-97, February.
    18. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.
    19. Diego Restrepo-Tobón & Subal Kumbhakar, 2015. "Nonparametric estimation of returns to scale using input distance functions: an application to large U.S. banks," Empirical Economics, Springer, vol. 48(1), pages 143-168, February.
    20. Tabri, Rami V., 2015. "Empirical Likelihood for Robust Poverty Comparisons," Working Papers 2015-02, University of Sydney, School of Economics, revised May 2015.

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    Keywords

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