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A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data

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  • Lv, Jing
  • Guo, Chaohui
  • Yang, Hu
  • Li, Yalian

Abstract

It is well known that the composite quantile regression is a very useful tool for regression analysis. In longitudinal studies, it requires a correct specification of the covariance structure to obtain efficient estimation of the regression coefficients. However, it is a challenging task to specify the correlation matrix in composite quantile regression with longitudinal data. In this paper, we develop a new regression model to parameterize covariance structures by utilizing the modified Cholesky decomposition. Then, based on the estimated covariance matrix, efficient composite quantile estimating functions are constructed to produce more efficient estimates. Since the proposed estimating functions are discrete and non-convex, we apply the induced smoothing approach to achieve fast and accurate estimation of the regression coefficients. Furthermore, we derive the asymptotic distributions of the parameter estimations both in mean and covariance models. Finally, simulations and a real data analysis have demonstrated the robustness and efficiency of the proposed approach.

Suggested Citation

  • Lv, Jing & Guo, Chaohui & Yang, Hu & Li, Yalian, 2017. "A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 129-144.
    • Handle: RePEc:eee:csdana:v:112:y:2017:i:c:p:129-144
    DOI: 10.1016/j.csda.2017.02.015
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    References listed on IDEAS

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    Cited by:

    1. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    2. Jing Lv & Chaohui Guo, 2019. "Quantile estimations via modified Cholesky decomposition for longitudinal single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1163-1199, October.
    3. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.

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