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Efficient parameter estimation via Gaussian copulas for quantile regression with longitudinal data

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  • Fu, Liya
  • Wang, You-Gan

Abstract

Specifying a correlation matrix is challenging in quantile regression with longitudinal data. A naive method is simply to adopt an independence working model. However, the efficiency of parameter estimates may be lost. We propose constructing a working correlation matrix via Gaussian copula which can handle or incorporate general serial dependence. A suit of unbiased estimating functions can be obtained by assuming the Gaussian copula with different correlation matrices, and the empirical likelihood method can then combine these unbiased estimating functions. Furthermore, the induced smoothing approach is applied to the discontinuous estimating functions to reduce computation burdens. The asymptotic normality of the resulting estimators is established. Simulation studies indicate that the proposed method is superior to the alternative estimating functions especially when the working correlation matrix is misspecified. Finally, a real dataset from forced expiratory volume study is used to illustrate the proposed method.

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  • Fu, Liya & Wang, You-Gan, 2016. "Efficient parameter estimation via Gaussian copulas for quantile regression with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 492-502.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:492-502
    DOI: 10.1016/j.jmva.2015.07.004
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    Cited by:

    1. 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.
    2. Stanislav Anatolyev & Vladimir Pyrlik, 2021. "Shrinkage for Gaussian and t Copulas in Ultra-High Dimensions," CERGE-EI Working Papers wp699, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    3. Jing Lv & Chaohui Guo, 2017. "Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data," Computational Statistics, Springer, vol. 32(3), pages 947-975, September.
    4. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    5. Kangning Wang & Wen Shan, 2021. "Copula and composite quantile regression-based estimating equations for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 441-455, June.
    6. Anatolyev, Stanislav & Pyrlik, Vladimir, 2022. "Copula shrinkage and portfolio allocation in ultra-high dimensions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    7. Kangning Wang & Xiaofei Sun, 2020. "Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data," Statistical Papers, Springer, vol. 61(3), pages 967-995, June.
    8. Jing Lv & Chaohui Guo & Jibo Wu, 2019. "Smoothed empirical likelihood inference via the modified Cholesky decomposition for quantile varying coefficient models with longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 999-1032, September.

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