Semiparametric partially linear regression models for functional data

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• 作者：Tao Zhang^a ; ^b ; Qihua Wang^a ; ^c ; ^{qhwang@amss.ac.cn}
• 关键词：Longitudinal data ; Functional data ; Semiparametric partially linear regression models ; Asymptotic normality
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2012
• 期刊代码：36_03783758
• 类别：mt
• 出版时间：September, 2012
• 卷：142
• 期：9
• 页码：2518-2529
• 文件大小：240 K

摘要

In the context of longitudinal data analysis, a random function typically represents a subject that is often observed at a small number of time point. For discarding this restricted condition of observation number of each subject, we consider the semiparametric partially linear regression models with mean function + g(z), where x and z are functional data. The estimations of and g(z) are presented and some asymptotic results are given. It is shown that the estimator of the parametric component is asymptotically normal. The convergence rate of the estimator of the nonparametric component is also obtained. Here, the observation number of each subject is completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.