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Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

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  • JIANHUA Z. HUANG
  • LIANGYUE ZHANG
  • LAN ZHOU

Abstract

. We consider marginal semiparametric partially linear models for longitudinal/clustered data and propose an estimation procedure based on a spline approximation of the non‐parametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). Our estimates of both parametric part and non‐parametric part of the model have properties parallel to those of parametric GEE, that is, the estimates are efficient if the covariance structure is correctly specified and they are still consistent and asymptotically normal even if the covariance structure is misspecified. By showing that our estimate achieves the semiparametric information bound, we actually establish the efficiency of estimating the parametric part of the model in a stronger sense than what is typically considered for GEE. The semiparametric efficiency of our estimate is obtained by assuming only conditional moment restrictions instead of the strict multivariate Gaussian error assumption.

Suggested Citation

  • Jianhua Z. Huang & Liangyue Zhang & Lan Zhou, 2007. "Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 451-477, September.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:3:p:451-477
    DOI: 10.1111/j.1467-9469.2006.00550.x
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    Citations

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    Cited by:

    1. Minggen Lu, 2017. "Efficient estimation of quasi-likelihood models using B-splines," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1099-1127, October.
    2. Zou, Yubo & Zhang, Jiajia & Qin, Guoyou, 2011. "A semiparametric accelerated failure time partial linear model and its application to breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1479-1487, March.
    3. Xu, Peirong & Peng, Heng & Huang, Tao, 2018. "Unsupervised learning of mixture regression models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 44-56.
    4. Chen, Huaihou & Paik, Myunghee Cho & Dhamoon, Mandip S. & Moon, Yeseon Park & Willey, Joshua & Sacco, Ralph L. & Elkind, Mitchell S.V., 2012. "Semiparametric model for the dichotomized functional outcome after stroke: The Northern Manhattan Study," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2598-2608.
    5. Peirong Xu & Jun Zhang & Xingfang Huang & Tao Wang, 2016. "Efficient estimation for marginal generalized partially linear single-index 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. 25(3), pages 413-431, September.
    6. Weihua Zhao & Weiping Zhang & Heng Lian, 2020. "Marginal quantile regression for varying coefficient models with longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 213-234, February.
    7. Haibo Zhou & Guoyou Qin & Matthew P. Longnecker, 2011. "A Partial Linear Model in the Outcome-Dependent Sampling Setting to Evaluate the Effect of Prenatal PCB Exposure on Cognitive Function in Children," Biometrics, The International Biometric Society, vol. 67(3), pages 876-885, September.
    8. Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2016. "Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 24-39.
    9. Guoyou Qin & Zhongyi Zhu & Wing Fung, 2012. "Robust estimation of the generalised partial linear model with missing covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 517-530.
    10. 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.

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