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Adapting Kernel Estimation to Uncertain Smoothness

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  • Yulia Kotlyarova
  • Marcia M Schafgans
  • Victoria Zinde-Walsh

Abstract

For local and average kernel based estimators, smoothness conditions ensure that the kernel order determines the rate at which the bias of the estimator goes to zero and thus allows the econometrician to control the rate of convergence. In practice, even with smoothness the estimation errors may be substantial and sensitive to the choice of the bandwidth and kernel. For distributions that do not have sufficient smoothness asymptotic theory may importantly differ from standard; for example, there may be no bandwidth for which average estimators attain root-n consistency. We demonstrate that non-convex combinations of estimators computed for different kernel/bandwidth pairs can reduce the trace of asymptotic mean square error relative even to the optimal kernel/bandwidth pair. Our combined estimator builds on these results. To construct it we provide new general estimators for degree of smoothness, optimal rate and for the biases and covariances of estimators. We show that a bootstrap estimator is consistent for the variance of local estimators but exhibits a large bias for the average estimators; a suitable adjustment is provided.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2011/557.

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Date of creation: Apr 2011
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Handle: RePEc:cep:stiecm:/2011/557

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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Keywords: Nonparametric estimation; kernel based estimator; combined stimator; variance bootstrap.;

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  1. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Robust Kernel Estimator For Densities Of Unknown," Departmental Working Papers 2005-05, McGill University, Department of Economics.
  2. Donkers, Bas & Schafgans, Marcia, 2008. "Specification And Estimation Of Semiparametric Multiple-Index Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1584-1606, December.
  3. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
  4. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
  5. John DiNardo & Justin L. Tobias, 2001. "Nonparametric Density and Regression Estimation," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 11-28, Fall.
  6. Haerdle,W. Hildenbrand,W. Jerison,M., 1988. "Empirical evidence on the law of demand," Discussion Paper Serie A 193, University of Bonn, Germany.
  7. Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2010. "Smoothness adaptive average derivative estimation," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 40-62, 02.
  8. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1031-1057, December.
  9. Huynh, Kim P. & Jacho-Chávez, David T., 2009. "Growth and governance: A nonparametric analysis," Journal of Comparative Economics, Elsevier, vol. 37(1), pages 121-143, March.
  10. Kotlyarova, Yulia & Zinde-Walsh, Victoria, 2006. "Non- and semi-parametric estimation in models with unknown smoothness," Economics Letters, Elsevier, vol. 93(3), pages 379-386, December.
  11. Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2010. "Bootstrapping Density-Weighted Average Derivatives," CREATES Research Papers 2010-23, School of Economics and Management, University of Aarhus.
  12. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
  13. Daniel J. Henderson & Daniel L. Millimet, 2008. "Is gravity linear?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 137-172.
  14. Richard Blundell & Alan Duncan, 1998. "Kernel Regression in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 62-87.
  15. Calabrese, Raffaella & Zenga, Michele, 2010. "Bank loan recovery rates: Measuring and nonparametric density estimation," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 903-911, May.
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