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Consistency of nonlinear regression quantiles under Type I censoring weak dependence and general covariate design

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  • Oberhofer, Walter
  • Haupt, Harry

Abstract

For both deterministic or stochastic regressors, as well as parametric nonlinear or linear regression functions, we prove the weak consistency of the coefficient estimators for the Type I censored quantile regression model under different censoring mechanisms with censoring points depending on the observation index (in a nonstochastic manner) and a weakly dependent error process. Our argumentation is based on an exposition of the connection between the residuals of the economically relevant model at the outset of the censored regression problem, and the residuals which are subject to the corresponding optimization process of censored quantile regression. In dieser Arbeit wird die schwache Konsistenz der Koeffizientenschätzer für das zensierte (Typ I) Quantilsregressionsmodell unter sehr allgemeinen Bedingungen -- lineare und nichtlineare Regressionsfunktionen, deterministische und stochastische Regressoren, Zensierungsgrenzen die (in nichtstochastischer Weise) vom Beobachtungsindex abhängen sowie schwach abhängige Fehlerterme -- bewiesen. Die Argumentation basiert dabei auf dem Zusammenhang zwischen den ökonomischen relevanten Residuen des Ausgangsmodells und den Residuen die Gegenstand der Zielfunktion des Optimierungskalküls der zensierten Quantilsregression sind.

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File URL: http://epub.uni-regensburg.de/4521/1/DP406_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 406.

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Date of creation: 2005
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Handle: RePEc:bay:rdwiwi:480

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Keywords: Quantil ; Nichtlineare Regression; Typ I Zensierung; Quantile regression ; nonlinear regression ; Type I censoring;

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  1. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 169-192, February.
  2. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 653-672, May.
  3. Arthur Lewbel & Oliver Linton, 2000. "Nonparametric censored and truncated regression," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2060, London School of Economics and Political Science, LSE Library.
  4. Mukherjee, Kanchan, 2000. "Linearization Of Randomly Weighted Empiricals Under Long Range Dependence With Applications To Nonlinear Regression Quantiles," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(03), pages 301-323, June.
  5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
  6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521586115.
  7. Bilias, Yannis & Chen, Songnian & Ying, Zhiliang, 2000. "Simple resampling methods for censored regression quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 99(2), pages 373-386, December.
  8. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
  9. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, Elsevier, vol. 71(1-2), pages 265-283.
  10. Khan, Shakeeb & Powell, James L., 2001. "Two-step estimation of semiparametric censored regression models," Journal of Econometrics, Elsevier, Elsevier, vol. 103(1-2), pages 73-110, July.
  11. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, Elsevier, vol. 25(3), pages 303-325, July.
  12. Chen, Songnian & Khan, Shakeeb, 2000. "Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 98(2), pages 283-316, October.
  13. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 32(1), pages 143-155, June.
  14. Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, Elsevier, vol. 68(3), pages 235-245, July.
  15. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 295-317, September.
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