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Asymptotic behavior of regression quantiles in non-stationary, dependent cases


  • Portnoy, Stephen


Regression quantiles provide a natural and powerful approach for robust analysis of the general linear model. However, departures from independence and stationarity of the errors can have an extremely potent effect on statistical analysis. Here, a Bahadur representation for regression quantiles is provided for error processes which are highly non-stationary (i.e., for which there is a nonvanishing bias term) and which are close to being m-dependent. The conditions for dependence are based on a decomposition of Chanda, Puri, and Ruymgaart which covers linear processes; and, hence, includes ARMA processes.

Suggested Citation

  • Portnoy, Stephen, 1991. "Asymptotic behavior of regression quantiles in non-stationary, dependent cases," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 100-113, July.
  • Handle: RePEc:eee:jmvana:v:38:y:1991:i:1:p:100-113

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    References listed on IDEAS

    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
    3. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
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    Cited by:

    1. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639,
    2. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    3. George Kouretas & Leonidas Zarangas, 2005. "Conditional autoregressive valu at risk by regression quantile: Estimatingmarket risk for major stock markets," Working Papers 0521, University of Crete, Department of Economics.
    4. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    5. Alexandre Belloni & Victor Chernozhukov, 2009. "L1-Penalized Quantile Regression in High-Dimensional Sparse Models," Papers 0904.2931,, revised Nov 2011.
    6. 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.
    7. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
    8. Neocleous, Tereza & Portnoy, Stephen, 2008. "On monotonicity of regression quantile functions," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1226-1229, August.
    9. Gounder, Rukmani & Xing, Zhongwei, 2012. "Impact of education and health on poverty reduction: Monetary and non-monetary evidence from Fiji," Economic Modelling, Elsevier, vol. 29(3), pages 787-794.
    10. Élise, COUDIN & Jean-Marie DUFOUR, 2017. "Finite-Sample Generalized Confidence Distributions and Sign-Based Robust Estimators in Median Regressions with Heterogeneous Dependent Errors," Cahiers de recherche 01-2017, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    12. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    13. Rima Rajab & Milan Dražić & Nenad Mladenović & Pavle Mladenović & Keming Yu, 2015. "Fitting censored quantile regression by variable neighborhood search," Journal of Global Optimization, Springer, vol. 63(3), pages 481-500, November.
    14. Tae-Hwan Kim, & Christophe Muller, 2012. "Bias Transmission and Variance Reduction in Two-Stage Quantile Regression," AMSE Working Papers 1221, Aix-Marseille School of Economics, Marseille, France.
    15. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
    16. Seokwoo Jake Choi & Stephen Portnoy, 2016. "Quantile Autoregression for Censored Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 603-623, September.
    17. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
    18. B. Dima & Ş. M. Dima, 2016. "Income Distribution and Social Tolerance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 128(1), pages 439-466, August.
    19. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, Elsevier.
    20. Fitzenberger, Bernd, 1994. "A note on estimating censored quantile regressions," Discussion Papers 14, University of Konstanz, Center for International Labor Economics (CILE).
    21. repec:eee:ecmode:v:64:y:2017:i:c:p:48-59 is not listed on IDEAS


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