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Focused information criterion and model averaging based on weighted composite quantile regression

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  • Ganggang Xu
  • Suojin Wang
  • Jianhua Z. Huang

Abstract

type="main" xml:id="sjos12034-abs-0001"> We study the focused information criterion and frequentist model averaging and their application to post-model-selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models. With the non-parametric functions approximated by polynomial splines, we show that, under certain conditions, the asymptotic distribution of the frequentist model averaging WCQR-estimator of a focused parameter is a non-linear mixture of normal distributions. This asymptotic distribution is used to construct confidence intervals that achieve the nominal coverage probability. With properly chosen weights, the focused information criterion based WCQR estimators are not only robust to outliers and non-normal residuals but also can achieve efficiency close to the maximum likelihood estimator, without assuming the true error distribution. Simulation studies and a real data analysis are used to illustrate the effectiveness of the proposed procedure.

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  • Ganggang Xu & Suojin Wang & Jianhua Z. Huang, 2014. "Focused information criterion and model averaging based on weighted composite quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 365-381, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:365-381
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    File URL: http://hdl.handle.net/10.1111/sjos.12034
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    2. Peixin Zhao & Xiaoshuang Zhou, 2018. "Robust empirical likelihood for partially linear models via weighted composite quantile regression," Computational Statistics, Springer, vol. 33(2), pages 659-674, June.
    3. Xu, Ganggang & Genton, Marc G., 2015. "Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 78-91.
    4. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    5. Jiang Du & Zhongzhan Zhang & Tianfa Xie, 2017. "Focused information criterion and model averaging in censored quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 547-570, July.
    6. Zhang, Qingzhao & Duan, Xiaogang & Ma, Shuangge, 2017. "Focused information criterion and model averaging with generalized rank regression," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 11-19.

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