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Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints

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

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.

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File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2012-08.pdf
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Paper provided by McMaster University in its series Department of Economics Working Papers with number 2012-08.

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Length: 47 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:mcm:deptwp:2012-08
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  1. Francisca Galindo-Garre & Jeroen Vermunt, 2004. "The order-restricted association model: Two estimation algorithms and issues in testing," Psychometrika, Springer, vol. 69(4), pages 641-654, December.
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  7. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
  8. Shujie Ma & Jeffrey S. Racine, 2012. "Additive Regression Splines With Irrelevant Categorical and Continuous Regressors," Department of Economics Working Papers 2012-07, McMaster University.
  9. Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-27, September.
  10. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  11. Enno MAMMEN & C. THOMAS-AGNAN, 1996. "Smoothing Splines And Shape Restrictions," SFB 373 Discussion Papers 1996,87, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  13. E. Mammen, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252.
  14. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
  15. Gallant, A. Ronald, 1982. "Unbiased determination of production technologies," Journal of Econometrics, Elsevier, vol. 20(2), pages 285-323, November.
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