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Penalized quadratic inference functions for single-index models with longitudinal data

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  • Bai, Yang
  • Fung, Wing K.
  • Zhu, Zhong Yi

Abstract

In this paper, we focus on single-index models for longitudinal data. We propose a procedure to estimate the single-index component and the unknown link function based on the combination of the penalized splines and quadratic inference functions. It is shown that the proposed estimation method has good asymptotic properties. We also evaluate the finite sample performance of the proposed method via Monte Carlo simulation studies. Furthermore, the proposed method is illustrated in the analysis of a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:152-161
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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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Annie Qu & Bruce G. Lindsay, 2003. "Building adaptive estimating equations when inverse of covariance estimation is difficult," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 127-142, February.
    4. Xihong Lin, 2004. "Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data," Biometrika, Biometrika Trust, vol. 91(1), pages 177-193, March.
    5. Carro, Jesus M., 2007. "Estimating dynamic panel data discrete choice models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 503-528, October.
    6. 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.
    7. Yang Bai & Zhongyi Zhu & Wing K. Fung, 2008. "Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 104-118, March.
    8. Yuan, Ke-Hai, 1997. "A Theorem on Uniform Convergence of Stochastic Functions with Applications," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 100-109, July.
    9. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    10. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
    11. Annie Qu & Runze Li, 2006. "Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(2), pages 379-391, June.
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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. 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.
    4. 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.
    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. 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. 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.
    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. 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.
    10. Li, Daoji & Pan, Jianxin, 2013. "Empirical likelihood for generalized linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 63-73.
    11. Pang, Zhen & Xue, Liugen, 2012. "Estimation for the single-index models with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1837-1853.
    12. 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.

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