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Model-Robust Designs for Quantile Regression

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  • Linglong Kong
  • Douglas P. Wiens

Abstract

We give methods for the construction of designs for regression models, when the purpose of the investigation is the estimation of the conditional quantile function, and the estimation method is quantile regression. The designs are robust against misspecified response functions, and against unanticipated heteroscedasticity. The methods are illustrated by example, and in a case study in which they are applied to growth charts.

Suggested Citation

  • Linglong Kong & Douglas P. Wiens, 2015. "Model-Robust Designs for Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 233-245, March.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:509:p:233-245
    DOI: 10.1080/01621459.2014.969427
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    References listed on IDEAS

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    1. Rubia, Antonio & Sanchis-Marco, Lidia, 2013. "On downside risk predictability through liquidity and trading activity: A dynamic quantile approach," International Journal of Forecasting, Elsevier, vol. 29(1), pages 202-219.
    2. Pengfei Li & Douglas P. Wiens, 2011. "Robustness of design in dose–response studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 215-238, March.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    4. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.
    5. Holger Dette & Matthias Trampisch, 2012. "Optimal Designs for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1140-1151, September.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Wiens, Douglas P. & Wu, Eden K.H., 2010. "A comparative study of robust designs for M-estimated regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1683-1695, June.
    8. Wiens, Douglas P., 1991. "Designs for approximately linear regression: two optimality properties of uniform designs," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 217-221, September.
    9. Kaishev, V. K., 1989. "Optimal experimental designs for the B-spline regression," Computational Statistics & Data Analysis, Elsevier, vol. 8(1), pages 39-47, May.
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    Cited by:

    1. Peng, Cheng & Kouri, Drew P. & Uryasev, Stan, 2024. "Efficient and robust optimal design for quantile regression based on linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    2. Kai Yzenbrandt & Julie Zhou, 2022. "Minimax robust designs for regression models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 203-222, February.

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