Joint semiparametric mean-covariance model in longitudinal study
Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semipar...
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| Published in | Science China. Mathematics Vol. 54; no. 1; pp. 145 - 164 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
SP Science China Press
01.01.2011
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-7283 1869-1862 |
| DOI | 10.1007/s11425-010-4078-4 |
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| Abstract | Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach. |
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| AbstractList | Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach. |
| Author | Zhu, ZhongYi Mao, Jie |
| Author_xml | – sequence: 1 givenname: Jie surname: Mao fullname: Mao, Jie organization: Department of Statistics, Fudan University – sequence: 2 givenname: ZhongYi surname: Zhu fullname: Zhu, ZhongYi email: zhuzy@fudan.edu.cn organization: Department of Statistics, Fudan University |
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| CitedBy_id | crossref_primary_10_12677_SA_2020_95094 crossref_primary_10_1016_j_jkss_2016_10_003 crossref_primary_10_1007_s11425_016_0126_3 crossref_primary_10_1080_02664763_2014_920778 |
| Cites_doi | 10.1214/09-AOS695 10.1198/016214504000001060 10.1093/biomet/89.3.579 10.2307/2532783 10.1198/016214508000000742 10.2307/2670121 10.2307/3109751 10.1093/biomet/93.4.927 10.1111/1467-9868.00233 10.1093/biomet/90.1.239 10.2307/2291516 10.1093/oso/9780198524847.001.0001 10.3150/bj/1137421639 10.1093/biomet/90.4.831 10.1093/biomet/87.2.425 10.1214/009053607000000523 10.1093/biomet/86.3.677 10.1093/biomet/73.1.13 10.1198/016214505000000277 10.1093/biomet/86.3.691 10.1093/biomet/89.1.111 10.1198/016214507000000095 |
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| Keywords | local linear regression semiparametric varying-coefficient partially linear model 62G08 62G20 generalized estimating equation 62F12 kernel estimation modified Cholesky decomposition |
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| Title | Joint semiparametric mean-covariance model in longitudinal study |
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