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Extremal quantile regression

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  • Victor Chernozhukov

Abstract

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically, it obtains the large sample properties of extremal (extreme order and intermediate order) quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values. This modeling setup combines restrictions of extreme value theory with leading homoscedastic and heteroscedastic linear specifications of regression analysis. In large samples, extreme order regression quantiles converge weakly to \argmin functionals of stochastic integrals of Poisson processes that depend on regressors, while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design.

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  • Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
  • Handle: RePEc:arx:papers:math/0505639
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    File URL: http://arxiv.org/pdf/math/0505639
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    References listed on IDEAS

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    3. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
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    6. Jason Abrevaya, 2001. "The effects of demographics and maternal behavior on the distribution of birth outcomes," Empirical Economics, Springer, vol. 26(1), pages 247-257.
    7. Donald, Stephen G & Paarsch, Harry J, 1993. "Piecewise Pseudo-maximum Likelihood Estimation in Empirical Models of Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 121-148, February.
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    Cited by:

    1. Saul Lach & José L. Moraga†González, 2017. "Asymmetric Price Effects of Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 65(4), pages 767-803, December.
    2. Eric Blankmeyer, 2012. "Estimating an inflation index by quantile regression," Applied Economics Letters, Taylor & Francis Journals, vol. 19(2), pages 185-187, February.
    3. Lach, Saul & Moraga-González, José-Luis, 2009. "Heterogeneous Price Information and the Effect of Competition," CEPR Discussion Papers 7319, C.E.P.R. Discussion Papers.
    4. D’Haultfœuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2018. "Extremal quantile regressions for selection models and the black–white wage gap," Journal of Econometrics, Elsevier, vol. 203(1), pages 129-142.
    5. Alexandre Belloni & Victor Chernozhukov, 2009. "L1-Penalized Quantile Regression in High-Dimensional Sparse Models," Papers 0904.2931, arXiv.org, revised Nov 2011.
    6. Calluzzo, Paul & Dong, Gang Nathan, 2015. "Has the financial system become safer after the crisis? The changing nature of financial institution risk," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 233-248.
    7. repec:gam:jrisks:v:5:y:2017:i:3:p:38-:d:105140 is not listed on IDEAS
    8. Patrick Bajari & Han Hong & Minjung Park & Robert Town, 2011. "Regression Discontinuity Designs with an Endogenous Forcing Variable and an Application to Contracting in Health Care," NBER Working Papers 17643, National Bureau of Economic Research, Inc.
    9. Gonzalo, Jesús & Dolado Lobregad, Juan José & Chen, Liang, 2017. "Quantile Factor Models," UC3M Working papers. Economics 25299, Universidad Carlos III de Madrid. Departamento de Economía.
    10. Carlos Martins-Filho & Feng Yao & Maximo Torero, 2015. "High-Order Conditional Quantile Estimation Based on Nonparametric Models of Regression," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 907-958, December.
    11. Qi Zheng & Colin Gallagher & K.B. Kulasekera, 2013. "Adaptively weighted kernel regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 855-872, December.
    12. Philippe Van Kerm & Seunghee Yu & Chung Choe, 2016. "Decomposing quantile wage gaps: a conditional likelihood approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(4), pages 507-527, August.

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