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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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    1. You-Gan Wang & Xu Lin & Min Zhu, 2005. "Robust Estimating Functions and Bias Correction for Longitudinal Data Analysis," Biometrics, The International Biometric Society, vol. 61(3), pages 684-691, September.
    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. 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.
    4. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
    5. 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.
    6. 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.
    7. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    8. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    9. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    10. Oman, Samuel D., 2009. "Easily simulated multivariate binary distributions with given positive and negative correlations," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 999-1005, February.
    11. 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.
    12. 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.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    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. 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.
    10. 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.
    11. 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.

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