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Regression Quantiles: An Example of Bicriteria Optimization

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Book cover Decision Making with Multiple Objectives

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 242))

Abstract

Regression quantiles are a robust alternative to the popular least squares regression and provide good descriptive statistics for the data. In this paper, we show that the problem to find regression quantiles associated with a data set can be formulated as a bicriteria optimization problem and solved by a simple algorithm that combines parametric programming with the simplex algorithm. We illustrate the proposed algorithm with a simple example.

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References

  • Bassett, G. W. and Koenker, R. W. (1982). An empirical quantile function for linear models with iid errors. J. Amer. Statist. Assoc., 77, 407–415.

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  • Koenker, R. W. and Bassett, G. W. (1978). Regression quantiles. Econometrics, 46, 33–50.

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  • Narula, S. C. and Wellington, J. W. (1984). Regression quantiles using bieriteria optimization. Report No. 10, Institute of Statistics, Virginia Commonwealth University, Richmond, Virginia.

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  • Ruppert, D. and Carroll, R. J. (1980). Trimmed least squares estimation in the linear model. J. Amer. Statist. Assoc, 75, 828–838.

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  • Wellington, J. F. and Narula, S. C. (1984). An algorithm for quantile regression, Communications in Statistics, Series B, 13, 683–704.

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Author information

Authors and Affiliations

  1. Virginia Commonwealth University, Richmond, Virginia, USA

    Subhash C. Narula

  2. Gannon University, Erie, Pennsylvania, USA

    John F. Wellington

Authors
  1. Subhash C. Narula
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  2. John F. Wellington
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Editor information

Editors and Affiliations

  1. Systems Engineering Department, Case Institute of Technology, Case Western Reserve University, Cleveland, Ohio, 44106, USA

    Yacov Y. Haimes  & Vira Chankong  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Narula, S.C., Wellington, J.F. (1985). Regression Quantiles: An Example of Bicriteria Optimization. In: Haimes, Y.Y., Chankong, V. (eds) Decision Making with Multiple Objectives. Lecture Notes in Economics and Mathematical Systems, vol 242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46536-9_40

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  • DOI: https://doi.org/10.1007/978-3-642-46536-9_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15223-1

  • Online ISBN: 978-3-642-46536-9

  • eBook Packages: Springer Book Archive

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