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Estimation for a marginal generalized single-index longitudinal model

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  • Xu, Peirong
  • Zhu, Lixing

Abstract

In this paper, we suggest an estimating equations based approach to study a general single-index model with a given out-layer link for longitudinal data and treat the classical one as its special case. Within a wide range of bandwidths which is for estimating the inner-layer nonparametric link, the root-n consistency of the estimator of the index can be proved. The estimation efficiency can be achieved even when there is an infinite-dimensional nuisance parameter to be estimated. The performance of the new method is assessed through the comparison with other existing methods and through an application to an epileptic seizure study.

Suggested Citation

  • Xu, Peirong & Zhu, Lixing, 2012. "Estimation for a marginal generalized single-index longitudinal model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 285-299.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:285-299
    DOI: 10.1016/j.jmva.2011.10.004
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    References listed on IDEAS

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    Cited by:

    1. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    2. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    3. Yongjin Li & Qingzhao Zhang & Qihua Wang, 2017. "Penalized estimation equation for an extended single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 169-187, February.
    4. 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.
    5. Jun Zhang & Zhenghui Feng & Xiaoguang Wang, 2018. "A constructive hypothesis test for the single-index models with two groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1077-1114, October.
    6. Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    7. 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.
    8. Shakhawat Hossain & Le An Lac, 2021. "Optimal shrinkage estimations in partially linear single-index models for binary longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 811-835, December.
    9. 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.
    10. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    11. 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.

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