Semiparametric partially linear regression models for functional data
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 wit...
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Published in | Journal of statistical planning and inference Vol. 142; no. 9; pp. 2518 - 2529 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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Elsevier B.V
01.09.2012
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ISSN | 0378-3758 1873-1171 |
DOI | 10.1016/j.jspi.2012.03.004 |
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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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AbstractList | 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. |
Author | Wang, Qihua Zhang, Tao |
Author_xml | – sequence: 1 givenname: Tao surname: Zhang fullname: Zhang, Tao organization: School of Mathematics and Statistics, Yunnan University, Kunming, China – sequence: 2 givenname: Qihua surname: Wang fullname: Wang, Qihua email: qhwang@amss.ac.cn organization: School of Mathematics and Statistics, Yunnan University, Kunming, China |
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Cites_doi | 10.1016/j.spl.2005.12.007 10.1198/016214501753208708 10.1198/016214504000001745 10.1214/009053604000001156 10.1016/j.jmva.2008.04.004 10.1111/j.1467-9469.2005.00429.x 10.1080/02331880801980377 10.3150/bj/1077544603 10.1214/11-AOS882 10.1214/09-AOS742 10.1080/01621459.1986.10478274 10.1214/009053606000000957 10.1198/jasa.2010.tm09313 10.1111/j.1467-9868.2005.00535.x 10.1198/016214504000001060 10.1214/aos/1176345455 10.1016/j.jmva.2007.04.010 10.1016/j.csda.2008.11.023 10.2307/2532783 10.1093/biomet/asp069 10.1016/j.jspi.2009.03.001 10.1111/j.1541-0420.2009.01293.x |
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Keywords | Semiparametric partially linear regression models Longitudinal data Functional data Asymptotic normality |
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