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Quadratic inference functions for partially linear single-index models with longitudinal data

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  • Lai, Peng
  • Li, Gaorong
  • Lian, Heng

Abstract

In this paper, we consider the partially linear single-index models with longitudinal data. We propose the bias-corrected quadratic inference function (QIF) method to estimate the parameters in the model by accounting for the within-subject correlation. Asymptotic properties for the proposed estimation methods are demonstrated. A generalized likelihood ratio test is established to test the linearity of the nonparametric part. Under the null hypotheses, the test statistic follows asymptotically a χ2 distribution. We also evaluate the finite sample performance of the proposed methods via Monte Carlo simulation studies and a real data analysis.

Suggested Citation

  • Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:115-127
    DOI: 10.1016/j.jmva.2013.03.019
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Green, Brittany & Lian, Heng & Yu, Yan & Zu, Tianhai, 2023. "Semiparametric penalized quadratic inference functions for longitudinal data in ultra-high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.
    3. 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.
    4. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    5. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    6. 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.
    7. Lei Liu & Zhihua Sun, 2017. "Kernel-based global MLE of partial linear random effects models for longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 615-635, July.
    8. Zhao, Weihua & Lian, Heng & Zhang, Riquan & Lai, Peng, 2016. "Estimation and variable selection for proportional response data with partially linear single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 40-56.
    9. Jun Zhang & Xia Cui & Heng Peng, 2020. "Estimation and hypothesis test for partial linear single-index multiplicative models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 699-740, June.

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