Geodesic
Empirical regression quantile processes
Applications of Mathematics, Tome 65 (2020) no. 3, pp. 257-269.

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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.
DOI : 10.21136/AM.2020.0295-19
Classification : 49M29, 62G30, 62J02, 65K05, 90C05
Keywords: averaged regression quantile; one-step regression quantile; $R$-estimator; functionals of the quantile process 
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Jurečková, Jana; Picek, Jan; Schindler, Martin. Empirical regression quantile processes. Applications of Mathematics, Tome 65 (2020) no. 3, pp. 257-269. doi : 10.21136/AM.2020.0295-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0295-19/

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