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Simultaneous confidence band for single-index random effects models with longitudinal data

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  • Yang, Suigen
  • Xue, Liugen
  • Li, Gaorong

Abstract

We get the estimator of the link function, establish the asymptotic properties, and construct the simultaneous confidence band for single-index random effects models. Simulation studies and real data set are presented to evaluate the performance of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:6-14
    DOI: 10.1016/j.spl.2013.10.014
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Li, Gaorong & Peng, Heng & Tong, Tiejun, 2013. "Simultaneous confidence band for nonparametric fixed effects panel data models," Economics Letters, Elsevier, vol. 119(3), pages 229-232.
    4. 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.
    5. Wu H. & Zhang J-T., 2002. "Local Polynomial Mixed-Effects Models for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 883-897, September.
    6. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    7. Zhang, Wenyang & Peng, Heng, 2010. "Simultaneous confidence band and hypothesis test in generalised varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1656-1680, August.
    8. 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.
    9. 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.
    10. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 928-955, November.
    11. Krivobokova, Tatyana & Kneib, Thomas & Claeskens, Gerda, 2010. "Simultaneous Confidence Bands for Penalized Spline Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 852-863.
    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.
    13. 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.
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    Cited by:

    1. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    2. Yiping Yang & Tiejun Tong & Gaorong Li, 2019. "SIMEX estimation for single-index model with covariate measurement error," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 137-161, March.

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