Regression Quantile and Averaged Regression Quantile Processes

  • Jana JurečkováEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 193)


We consider the averaged version \(\widetilde{B}_n(\alpha )\) of the two-step regression \(\alpha \)-quantile, introduced in [6] and studied in [7]. We show that it is asymptotically equivalent to the averaged version \(\bar{B}_n(\alpha )\) of ordinary regression quantile and also study the finite-sample relation of \(\widetilde{B}_n(\alpha )\) to \(\bar{B}_n(\alpha )\). An interest of its own has the fact that the vector of slope components of the regression \(\alpha \)-quantile coincides with a particular R-estimator of the slope components of regression parameter. Under a finite n,  the stochastic processes \(\widetilde{\mathscr {B}}_n=\{\widetilde{B}_n(\alpha ): \; 0<\alpha <1\}\) and \(\mathscr {B}_n=\{\bar{B}_n(\alpha ): \; 0<\alpha <1\}\) differ only by a drift.


Averaged regression quantile Regression quantile process Two-step regression quantile process 



The author’s research was supported by the Czech Republic Grant 15-00243S.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics, Department of Probability and StatisticsCharles UniversityPrague 8Czech Republic

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