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Assessing model adequacy in possibly misspecified quantile regression

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  • Noh, Hohsuk
  • El Ghouch, Anouar
  • Van Keilegom, Ingrid

Abstract

Possibly misspecified linear quantile regression models are considered. A measure for assessing the combined effect of several covariates on a certain conditional quantile function is proposed. The measure is based on an adaptation to quantile regression of the famous coefficient of determination originally proposed for mean regression, and compares a ‘reduced’ model to a ‘full’ model, both of which can be misspecified. An estimator of this measure is proposed and its asymptotic distribution is investigated both in the non-degenerate and the degenerate case. The finite sample performance of the estimator is studied through a number of simulation experiments. The proposed measure is also applied to a data set on body fat measures.

Suggested Citation

  • Noh, Hohsuk & El Ghouch, Anouar & Van Keilegom, Ingrid, 2013. "Assessing model adequacy in possibly misspecified quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 558-569.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:558-569
    DOI: 10.1016/j.csda.2012.07.020
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    References listed on IDEAS

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    1. Kani Chen & Zhiliang Ying & Hong Zhang & Lincheng Zhao, 2008. "Analysis of least absolute deviation," Biometrika, Biometrika Trust, vol. 95(1), pages 107-122.
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    3. McKean, Joseph W. & Sievers, Gerald L., 1987. "Coefficients of determination for least absolute deviation analysis," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 49-54, January.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Ruosha Li & Limin Peng, 2017. "Assessing quantile prediction with censored quantile regression models," Biometrics, The International Biometric Society, vol. 73(2), pages 517-528, June.
    2. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    3. Giessing, Alexander & He, Xuming, 2019. "On the predictive risk in misspecified quantile regression," Journal of Econometrics, Elsevier, vol. 213(1), pages 235-260.

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