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Estimation for the single-index models with random effects

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  • Pang, Zhen
  • Xue, Liugen

Abstract

In this paper, we generalize the single-index models to the scenarios with random effects. The introduction of the random effects raises interesting inferential challenges. Instead of treating the variance matrix as the tuning parameters in the nonparametric model of Gu and Ma (2005), we propose root-n consistent estimators for the variance components. Furthermore, the single-index part in our model avoids the curse of dimensionality and makes our model simpler. The variance components also cannot be treated as nuisance parameters and are canceled in the estimation procedure like Wang et al. (2010). A new set of estimating equations modified for the boundary effects is proposed to estimate the index coefficients. The link function is estimated by using the local linear smoother. Asymptotic normality is established for the proposed estimators. Also, the estimator of the link function achieves optimal convergence rate. These results facilitate the construction of confidence regions and hypothesis testing for the parameters of interest. Simulations show that our methods work well for high-dimensional p.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1837-1853
    DOI: 10.1016/j.csda.2011.11.007
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    References listed on IDEAS

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    Cited by:

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    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. Mahmoud, Hamdy F.F. & Kim, Inyoung, 2019. "Semiparametric spatial mixed effects single index models," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 108-122.
    5. 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.
    6. Hamdy F. F. Mahmoud & Inyoung Kim, 2023. "Semiparametric Integrated and Additive Spatio-Temporal Single-Index Models," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    7. Suli Cheng & Jianbao Chen, 2021. "Estimation of partially linear single-index spatial autoregressive model," Statistical Papers, Springer, vol. 62(1), pages 495-531, February.
    8. 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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