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Empirical likelihood based tests for detecting the presence of significant predictors in marginal quantile regression

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Listed:
  • Songqiao Tang

    (Zhejiang University)

  • Huiyu Wang

    (Zhejiang University)

  • Guanao Yan

    (Zhejiang University)

  • Lixin Zhang

    (Zhejiang University)

Abstract

This article investigates detecting the presence of significant predictors in marginal quantile regression. The main idea comes from the connection between the quantile correlation and the slope parameter of the marginal quantile regression, which is quite different from other methods. By introducing the local linear model and the plug-in empirical likelihood method, consistent asymptotic distribution and its adjusted version are obtained. We not only circumvent the non-regularity encountered by post-model-selected estimators but also make the results more concise. Two adaptive resampling test procedures are proposed in practice by comparing the t-statistics with a threshold to decide whether to use the traditional centered percentile bootstrap or otherwise adapt to the asymptotic distribution under the local model. Simulation studies compare these two resampling tests with other competing methods in several cases. Results show that the approaches proposed are more robust for each quantile level and can control type I error well. Two real datasets from Forbes magazine and the HIV drug resistance database are also applied to illustrate the new methods.

Suggested Citation

  • Songqiao Tang & Huiyu Wang & Guanao Yan & Lixin Zhang, 2023. "Empirical likelihood based tests for detecting the presence of significant predictors in marginal quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 149-179, February.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:2:d:10.1007_s00184-022-00866-1
    DOI: 10.1007/s00184-022-00866-1
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    References listed on IDEAS

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    1. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    2. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Qi-Hua Wang & Bing-Yi Jing, 2001. "Empirical Likelihood for a Class of Functionals of Survival Distribution with Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 517-527, September.
    4. Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    5. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Shujie Ma & Runze Li & Chih-Ling Tsai, 2017. "Variable Screening via Quantile Partial Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 650-663, April.
    8. Ma, Xuejun & Zhang, Jingxiao, 2016. "Robust model-free feature screening via quantile correlation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 472-480.
    9. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    10. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    11. Huixia Judy Wang & Ian W. McKeague & Min Qian, 2018. "Testing for marginal linear effects in quantile regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 433-452, March.
    12. Cheng Yong Tang & Chenlei Leng, 2010. "Penalized high-dimensional empirical likelihood," Biometrika, Biometrika Trust, vol. 97(4), pages 905-920.
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