Semiparametric partially linear regression models for functional data |
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Authors: | Tao Zhang Qihua Wang |
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Institution: | 1. School of Mathematics and Statistics, Yunnan University, Kunming, China;2. Department of Information and Computation of Science, Guangxi University of Technology, Liuzhou, China;3. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China |
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Abstract: | 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 x?β + g(z), where x and z are functional data. The estimations of β 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. |
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Keywords: | Longitudinal data Functional data Semiparametric partially linear regression models Asymptotic normality |
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