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Minimax Regression Quantiles


  • Stefan Holst Bache

    () (Aarhus University, School of Economics and Management and CREATES)


A new and alternative quantile regression estimator is developed and it is shown that the estimator is root n-consistent and asymptotically normal. The estimator is based on a minimax ‘deviance function’ and has asymptotically equivalent properties to the usual quantile regression estimator. It is, however, a different and therefore new estimator. It allows for both linear- and nonlinear model specifications. A simple algorithm for computing the estimates is proposed. It seems to work quite well in practice but whether it has theoretical justification is still an open question.

Suggested Citation

  • Stefan Holst Bache, 2010. "Minimax Regression Quantiles," CREATES Research Papers 2010-54, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-54

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    References listed on IDEAS

    1. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
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    More about this item


    Quantile regression; non-linear quantile regression; estimating functions; minimax estimation; empirical process theory;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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