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Nonlinear quantile regression under dependence and heterogeneity

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  • Oberhofer, Walter
  • Haupt, Harry

Abstract

This paper derives the asymptotic normality of the nonlinear quantile regression estimator with dependent errors. The required assumptions are weak, and it is neither assumed that the error process is stationary nor that it is mixing. In fact, the notion of weak dependence introduced in this paper, can be considered as a quantile specific local variant of known concepts. The connection of the derived asymptotic results to corresponding results of least squares estimation is obvious. In dieser Arbeit wird die asymptotische Normalität des nichtlinearen Quantilsregressionsschätzers bei abhängigen Fehlertermen bewiesen. Die Annahmen die dabei zu Grunde liegen sind sehr schwach, wobei gezeigt wird, dass weder die Stationarität noch eine Mixing-Eigenschaft des Fehlerprozesses erforderlich sind. Von besonderer Bedeutung ist die in diesem Papier eingeführte quantilsspezifische Form von schwacher Abhängigkeit, die als lokale Variante existierender Konzepte interpretiert werden kann. Zudem zeigt sich, dass die Asymptotik starke Parallelen zum Fall der Minimumquadratschätzung aufweist.

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File URL: http://epub.uni-regensburg.de/4505/1/DP388_OH.pdf
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Bibliographic Info

Paper provided by University of Regensburg, Department of Economics in its series University of Regensburg Working Papers in Business, Economics and Management Information Systems with number 388.

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Date of creation: 2003
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Handle: RePEc:bay:rdwiwi:479

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Keywords: Quantil ; Nichtlineares Regressionsmodell ; Asymptotik; ; Quantile regression ; nonlinear regression ; asymptotics;

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  1. Zhao, Quanshui, 2001. "Asymptotically Efficient Median Regression In The Presence Of Heteroskedasticity Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 17(04), pages 765-784, August.
  2. Peter C.B. Phillips, 1990. "A Shortcut to LAD Estimator Asymptotics," Cowles Foundation Discussion Papers 949, Cowles Foundation for Research in Economics, Yale University.
  3. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(02), pages 210-230, August.
  4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, October.
  5. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, October.
  6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
  7. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(01), pages 46-68, March.
  8. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
  9. Mukherjee, Kanchan, 2000. "Linearization Of Randomly Weighted Empiricals Under Long Range Dependence With Applications To Nonlinear Regression Quantiles," Econometric Theory, Cambridge University Press, vol. 16(03), pages 301-323, June.
  10. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
  11. Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 235-245, July.
  12. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
  13. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  14. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(06), pages 995-1045, December.
  15. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
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