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Strong Consistency of Regression Quantiles and Related Empirical Processes

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  • Bassett, Gilbert W.
  • Koenker, Roger W.

Abstract

The strong consistency of regression quantile statistics (Koenker and Bassett [4]) in linear models with iid errors is established. Mild regularity conditions on the regression design sequence and the error distribution are required. Strong consistency of the associated empirical quantile process (introduced in Bassett and Koenker [1]) is also established under analogous conditions. However, for the proposed estimate of the conditional distribution function of Y, no regularity conditions on the error distribution are required for uniform strong convergence, thus establishing a Glivenko-Cantelli-type theorem for this estimator.

Suggested Citation

  • Bassett, Gilbert W. & Koenker, Roger W., 1986. "Strong Consistency of Regression Quantiles and Related Empirical Processes," Econometric Theory, Cambridge University Press, vol. 2(02), pages 191-201, August.
  • Handle: RePEc:cup:etheor:v:2:y:1986:i:02:p:191-201_01
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    References listed on IDEAS

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    1. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    2. Z. Lomnicki, 1961. "Tests for departure from normality in the case of linear stochastic processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 4(1), pages 37-62, December.
    3. Dhrymes, Phoebus J & Taylor, John B, 1976. "On an Efficient Two-Step Estimator for Dynamic Simultaneous Equations Models with Autoregressive Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 362-376, June.
    4. A. R. Pagan & A. D. Hall & P. K. Trivedi, 1983. "Assessing the Variability of Inflation," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 585-596.
    5. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    6. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Paolo Naticchioni & Andrea Ricci & Emiliano Rustichelli, 2007. "Wage Structure, Inequality And Skill-Biased Change: Is Italy An Outlier?," Quaderni del Dipartimento di Economia, Finanza e Statistica 38/2007, Università di Perugia, Dipartimento Economia.
    2. Juliana Guimarães & (Universidade NOVA de Lisboa, 2004. "Has long become longer or short become shorter? Evidence from a censored quantile regression analysis of the changes in the distribution of U.S. unemployment duration," Econometric Society 2004 Latin American Meetings 128, Econometric Society.
    3. Juan Manuel del Pozo Segura, 2017. " Has the Gender Wage Gap been Reduced during the 'Peruvian Growth Miracle?' A Distributional Approach," Documentos de Trabajo / Working Papers 2017-442, Departamento de Economía - Pontificia Universidad Católica del Perú.
    4. José Ferreira Machado & Pedro Portugal & Juliana Guimarães, 2006. "U.S. Unemployment Duration: Has Long Become Longer or Short Become Shorter?," Working Papers w200613, Banco de Portugal, Economics and Research Department.
    5. Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    6. Héctor Ricardo Gertel & Roberto Giuliodori & María Luz Vera & Guadalupe Bastos & Sonia Costanzo, 2010. "Heterogeneidad en el desempeño académico de los estudiantes de Argentina: evidencia a partir de regresión por cuantiles," Investigaciones de Economía de la Educación volume 5,in: María Jesús Mancebón-Torrubia & Domingo P. Ximénez-de-Embún & José María Gómez-Sancho & Gregorio Gim (ed.), Investigaciones de Economía de la Educación 5, edition 1, volume 5, chapter 6, pages 117-138 Asociación de Economía de la Educación.
    7. Yu, Chi Wai & Clarke, Bertrand, 2010. "Asymptotics of Bayesian median loss estimation," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1950-1958, October.
    8. Karun Adusumilli & Taisuke Otsu & Yoon-Jae Whang, 2017. "Inference on distribution functions under measurement error," STICERD - Econometrics Paper Series 594, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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