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Testing in linear composite quantile regression models

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  • Rong Jiang
  • Wei-Min Qian
  • Jing-Ru Li

Abstract

Composite quantile regression (CQR) can be more efficient and sometimes arbitrarily more efficient than least squares for non-normal random errors, and almost as efficient for normal random errors. Based on CQR, we propose a test method to deal with the testing problem of the parameter in the linear regression models. The critical values of the test statistic can be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and power evaluation is possible under the local alternatives. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from a walking behavior survey. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Rong Jiang & Wei-Min Qian & Jing-Ru Li, 2014. "Testing in linear composite quantile regression models," Computational Statistics, Springer, vol. 29(5), pages 1381-1402, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1381-1402
    DOI: 10.1007/s00180-014-0497-y
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    References listed on IDEAS

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    1. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
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    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, October.
    4. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    Cited by:

    1. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.

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