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Testing Additivity in Generalized Nonparametric Regression Models

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Abstract

We propose a nonparametric test of conditional independence based on the empirical distribution function. The asymptotic null distribution is a mixture of chi-squares. A bootstrap procedure is proposed for calculating the critical values. Our test has power against alternatives at distance n^{-1/2} from the null. Monte Carlo simulations provide evidence on size and power. We apply the test to the Boston housing dataset.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1106.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1106.

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Length: 37 pages
Date of creation: Jun 1995
Date of revision:
Publication status: Published in Journal of Econometrics (1999), 104: 1-48
Handle: RePEc:cwl:cwldpp:1106

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Conditional independence; empirical distribution; independence; nonparametric; smooth bootstrap; test;

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References

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  1. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  2. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  3. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," CORE Discussion Papers 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. L. YANG & Wolfgang HÄRDLE, 1996. "Nonparametric Autoregression with Multiplicative Volatility and Additive Mean," SFB 373 Discussion Papers 1996,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Lavergne, Pascal & Vuong, Quang, 1998. "Nonparametric significance testing," SFB 373 Discussion Papers 1998,75, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  7. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  8. Gozalo, Pedro L., 1993. "A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 451-477, June.
  9. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  10. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
  11. J. L. Horowitz, 1995. "Bootstrap Methods In Econometrics: Theory And Numerical Performance," SFB 373 Discussion Papers 1995,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  13. repec:wop:humbsf:1995-63 is not listed on IDEAS
  14. Wolfgang HÄRDLE & O. LINTON, 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  15. repec:wop:humbsf:1996-62 is not listed on IDEAS
  16. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.
  17. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  18. Azzalini,A. & Bowman,A.W. & Haerdle,W., 1988. "On the use of nonparametric regression for model checking," Discussion Paper Serie A 195, University of Bonn, Germany.
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Citations

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Cited by:
  1. Joris Pinkse, 2000. "Feasible Multivariate Nonparametric Estimation Using Weak Separability," Econometric Society World Congress 2000 Contributed Papers 1241, Econometric Society.

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