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Empirical Regression Quantile Processes

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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.

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Acknowledgement

We thank the reviewer for careful reading of our manuscript and for valuable comments.

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Authors and Affiliations

  1. Department of Probability and Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Jana Jurečková

  2. Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vodárenskou věží 4, 182 00, Praha 8, Czech Republic

    Jana Jurečková

  3. Department of Applied Mathematics, Technical University, Studentská 2, 461 17, Liberec, Czech Republic

    Jan Picek & Martin Schindler

Authors
  1. Jana Jurečková
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  2. Jan Picek
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  3. Martin Schindler
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Corresponding author

Correspondence to Martin Schindler.

Additional information

The authors gratefully acknowledge the support of the Grant GACR 18-01137S.

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Jurečková, J., Picek, J. & Schindler, M. Empirical Regression Quantile Processes. Appl Math 65, 257–269 (2020). https://doi.org/10.21136/AM.2020.0295-19

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  • DOI: https://doi.org/10.21136/AM.2020.0295-19

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