Estimation for the single-index models with random effects

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• 作者：Zhen Pang^a ; ^{zpang@ntu.edu.sg} ; Liugen Xue^b
• 关键词：Single-index models ; Mixed-effects models ; Local linear smoother ; Pooled estimator ; Variance components
• 刊名：Computational Statistics and Data Analysis
• 出版年：2012
• 期刊代码：19_01679473
• 类别：cp
• 出版时间：June, 2012
• 卷：56
• 期：6
• 页码：1837-1853
• 文件大小：476 K

摘要

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 , we propose root- 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 . 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 .