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Keywords:
averaged regression quantile; one-step regression quantile; $R$-estimator; functionals of the quantile process
averaged regression quantile; one-step regression quantile; $R$-estimator; functionals of the quantile process
Summary:
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.
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