Applications of Mathematics, Vol. 65, No. 3, pp. 257-269, 2020
Empirical regression quantile processes
Jana Jurečková, Jan Picek, Martin Schindler
Received November 8, 2019. Published online May 25, 2020.
Abstract: We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of various types in the situations with covariates.
Keywords: averaged regression quantile; one-step regression quantile; $R$-estimator; functionals of the quantile process
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Affiliations: Jana Jurečková, Department of Probability and Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic and The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodárenskou věží 4, 182 00 Praha 8, Czech Republic, e-mail: jurecko@karlin.mff.cuni.cz, jureckova@utia.cas.cz; Jan Picek, Martin Schindler (corresponding author), Department of Applied Mathematics, Technical University, Studentská 2, 461 17 Liberec, Czech Republic, e-mail: jan.picek@tul.cz, martin.schindler@tul.cz
