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Strong Consistency of Regression Quantiles and Related Empirical Processes

Author

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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(2), pages 191-201, August.
    • Handle: RePEc:cup:etheor:v:2:y:1986:i:02:p:191-201_01
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    1. Adusumilli, Karun & Kurisu, Daisuke & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," Journal of Econometrics, Elsevier, vol. 215(1), pages 131-164.
    2. 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.
    3. Sohag, Kazi & Kliestik, Tomas & Shams, S.M. Riad & Mariev, Oleg & Davidson, Natalia, 2022. "Capital market deepening, Governor’s characteristics and Russian regional enterprises: A big data analysis," Journal of Business Research, Elsevier, vol. 149(C), pages 340-352.
    4. 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.
    5. Pedro Portugal & José Ferreira Machado, 2006. "U.S. Unemployment Duration: Has Long Become Longer or Short Become Shorter?," Working Papers w200613, Banco de Portugal, Economics and Research Department.
    6. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
    7. Jungsik Noh & Sangyeol Lee, 2016. "Quantile Regression for Location-Scale Time Series Models with Conditional Heteroscedasticity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 700-720, September.
    8. 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.
    9. 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.
    10. 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.
    11. Adusumilli, Karun & Kurisu, Daisies & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," LSE Research Online Documents on Economics 102692, London School of Economics and Political Science, LSE Library.
    12. Yu, Chi Wai & Clarke, Bertrand, 2010. "Asymptotics of Bayesian median loss estimation," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1950-1958, October.
    13. Alexander Aue & Rex C. Y. Cheung & Thomas C. M. Lee & Ming Zhong, 2014. "Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1241-1256, September.

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