Estimation for the single-index models with random effects

Zhen Pang, Liugen Xue

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1837-1853
Number of pages17
JournalComputational Statistics and Data Analysis
Issue number6
Publication statusPublished - 1 Jun 2012
Externally publishedYes


  • Local linear smoother
  • Mixed-effects models
  • Pooled estimator
  • Single-index models
  • Variance components

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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