IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v25y2016i3d10.1007_s11749-015-0462-2.html
   My bibliography  Save this article

Efficient estimation for marginal generalized partially linear single-index models with longitudinal data

Author

Listed:
  • Peirong Xu

    (Southeast University)

  • Jun Zhang

    (Shenzhen University)

  • Xingfang Huang

    (Southeast University)

  • Tao Wang

    (Yale University)

Abstract

We consider marginal generalized partially linear single-index models for longitudinal data. A profile generalized estimating equations (GEE)-based approach is proposed to estimate unknown regression parameters. Within a wide range of bandwidths for estimating the nonparametric function, our profile GEE estimator is consistent and asymptotically normal even if the covariance structure is misspecified. Moreover, if the covariance structure is correctly specified, the semiparametric efficiency can be achieved under heteroscedasticity and without distributional assumptions on the covariates. Simulation studies are conducted to evaluate the finite sample performance of the proposed procedure. The proposed methodology is further illustrated through a data analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:3:d:10.1007_s11749-015-0462-2
    DOI: 10.1007/s11749-015-0462-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-015-0462-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-015-0462-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    3. 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.
    4. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    5. Yi, Grace Y. & He, Wenqing & Liang, Hua, 2009. "Analysis of correlated binary data under partially linear single-index logistic models," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 278-290, February.
    6. Bai, Yang & Fung, Wing K. & Zhu, Zhong Yi, 2009. "Penalized quadratic inference functions for single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 152-161, January.
    7. Xu, Jianwen & Wang, You-Gan, 2014. "Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 70-77.
    8. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    9. Yehua Li, 2011. "Efficient semiparametric regression for longitudinal data with nonparametric covariance estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 355-370.
    10. Grace Yi & Wenqing He & Hua Liang, 2011. "Semiparametric marginal and association regression methods for clustered binary data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 511-533, June.
    11. Zhang, Jun & Gai, Yujie & Wu, Ping, 2013. "Estimation in linear regression models with measurement errors subject to single-indexed distortion," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 103-120.
    12. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    13. 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.
    14. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    15. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    16. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    17. Chen, Kani & Jin, Zhezhen, 2006. "Partial Linear Regression Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 195-204, March.
    18. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
    5. Yang, Suigen & Xue, Liugen & Li, Gaorong, 2014. "Simultaneous confidence band for single-index random effects models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 6-14.
    6. Wu, Jingwei & Peng, Hanxiang & Tu, Wanzhu, 2019. "Large-sample estimation and inference in multivariate single-index models," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 382-396.
    7. 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.
    8. Jianglin Fang & Wanrong Liu & Xuewen Lu, 2018. "Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 255-281, April.
    9. 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.
    10. Jianhong Shi & Qian Yang & Xiongya Li & Weixing Song, 2017. "Effects of measurement error on a class of single-index varying coefficient regression models," Computational Statistics, Springer, vol. 32(3), pages 977-1001, September.
    11. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    12. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.
    13. S. Hossain & S. Ejaz Ahmed & Grace Y. Yi & B. Chen, 2016. "Shrinkage and pretest estimators for longitudinal data analysis under partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 531-549, September.
    14. Zhang, Junhua & Feng, Sanying & Li, Gaorong & Lian, Heng, 2011. "Empirical likelihood inference for partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 113(2), pages 165-167.
    15. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    16. 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.
    17. Li, Gaorong & Feng, Sanying & Peng, Heng, 2011. "A profile-type smoothed score function for a varying coefficient partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 372-385, February.
    18. Tang, Xingyu & Li, Jianbo & Lian, Heng, 2013. "Empirical likelihood for partially linear proportional hazards models with growing dimensions," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 22-32.
    19. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    20. Zhang, Jun & Gai, Yujie & Wu, Ping, 2013. "Estimation in linear regression models with measurement errors subject to single-indexed distortion," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 103-120.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:25:y:2016:i:3:d:10.1007_s11749-015-0462-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.