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A new local estimation method for single index models for longitudinal data

Author

Listed:
  • Hongmei Lin
  • Riquan Zhang
  • Jianhong Shi
  • Jicai Liu
  • Yanghui Liu

Abstract

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They are very useful for longitudinal data analysis. In this paper, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonparametric parts will be established. Monte Carlo simulation studies show excellent finite sample performance. Furthermore, we illustrate our methods with a real data example.

Suggested Citation

  • Hongmei Lin & Riquan Zhang & Jianhong Shi & Jicai Liu & Yanghui Liu, 2016. "A new local estimation method for single index models for longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 644-658, September.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:644-658
    DOI: 10.1080/10485252.2016.1191632
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    Cited by:

    1. 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.
    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. 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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