FUNCTIONAL SINGLE INDEX MODELS FOR LONGITUDINAL DATA

• 成果类型: Article
• 署名作者: Jiang, Ci-Ren; Wang, Jane-Ling
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS845
• 发表日期: 2011
• 页码: 362-388
• 关键词: projection pursuit regression; Dimension Reduction; asymptotic distributions; estimators

摘要

A new single-index model that reflects the time-dynamic effects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both longitudinal and time-invariant covariates. With appropriate initial estimates of the parametric index, the proposed estimator is shown to be root n-consistent and asymptotically normally distributed. We also address the nonparametric estimation of regression functions and provide estimates with optimal convergence rates. One advantage of the new approach is that the same bandwidth is used to estimate both the nonparametric mean function and the parameter in the index. The finite-sample performance for the proposed procedure is studied numerically.