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Averaged Regression Quantiles

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Book cover Contemporary Developments in Statistical Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 68))

Abstract

We show that weighted averaged regression α-quantile in the linear regression model, with regressor components as weights, is monotone in \(\alpha\in(0,1),\) and is asymptotically equivalent to the α-quantile of the location model. This relation remains true under the local heteroscedasticity of the model errors. As such, the averaged regression quantile provides various scale statistics, used for studentization and standardization in linear model, and an estimate of quantile density based on regression data. The properties are numerically illustrated.

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Acknowledgement

The authors thank the Editors for their assistance and the Referee for the careful reading the text. The research of J. Jurečková was supported by the Czech Republic Grant P201/12/0083. The research of Jan Picek was supported by the Czech Republic Grant P209/10/2045.

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Statistics, Charles University in Prague, Sokolovská 83, 186 75, Prague, Czech Republic

    Jana Jurečková

  2. Department of Applied Mathematics, Technical University in Liberec, Voroněžská 1329/13, 460 01, Liberec, Czech Republic

    Jan Picek

Authors
  1. Jana Jurečková
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  2. Jan Picek
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Corresponding author

Correspondence to Jana Jurečková .

Editor information

Editors and Affiliations

  1. North Carolina State Universy, Raleigh, North Carolina, USA

    Soumendra Lahiri

  2. Department of Mathematical Sciences, Binghampton University, Binghamton, New York, USA

    Anton Schick

  3. Applied Statistics Unit, Kolkata, India

    Ashis SenGupta

  4. Department of Statistics, University of Georgia, Athens, Georgia, USA

    T.N. Sriram

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Jurečková, J., Picek, J. (2014). Averaged Regression Quantiles. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_12

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