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An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models

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Author Info
Horowitz, Joel L. () (University of Iowa)
Spokoiny, Vladimir G. (Weierstrass Institute for Applied Analysis and Stochastics)
Abstract

This paper is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness. We develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate. The test accommodates conditional heteroskedasticity of unknown form. The numerical performance and usefulness of the test are illustrated by the results of Monte Carlo experiments and an empirical example.

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File URL: http://www.biz.uiowa.edu/econ/papers/uia/qtest.pdf
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Publisher Info
Paper provided by University of Iowa, Department of Economics in its series Working Papers with number 00-04.

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Length: 34 pages
Date of creation: Nov 2000
Date of revision:
Handle: RePEc:uia:iowaec:00-04

Contact details of provider:
Postal: University of Iowa, Department of Economics, Henry B. Tippie College of Business, Iowa City, Iowa 52242
Phone: (319) 335-0829
Fax: (319) 335-1956
Web page: http://tippie.uiowa.edu/economics/
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Related research
Keywords: Hypothesis testing; local alternative; uniform consistency;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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  4. Herman J. Bierens & Donna K. Ginther, 2001. "Integrated Conditional Moment testing of quantile regression models," Empirical Economics, Springer, vol. 26(1), pages 307-324. [Downloadable!] (restricted)
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    Other versions:
  6. Zheng, John Xu, 1998. "A Consistent Nonparametric Test Of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 14(01), pages 123-138, February. [Downloadable!]
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  8. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  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. [Downloadable!]
  10. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November. [Downloadable!] (restricted)
  11. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    Other versions:
  12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  13. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November. [Downloadable!] (restricted)
    Other versions:
  14. James M. Poterba & Kim S. Rueben, 1994. "The Distribution of Public Sector Wage Premia: New Evidence Using Quantile Regression Methods," NBER Working Papers 4734, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    Other versions:
  17. 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. [Downloadable!]
  18. 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. [Downloadable!] (restricted)
  19. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August. [Downloadable!] (restricted)
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