2009.46: Nonparametric Regression of Covariance Structures in Longitudinal Studies
2009.46: Jianxin Pan, Huajin Ye and Runze Li (2009) Nonparametric Regression of Covariance Structures in Longitudinal Studies.
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In this paper we propose a nonparametric data-driven approach to model covariance structures for longitudinal data. Based on a modi¯ed Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix in- volving generalized autoregressive coe±cients and a diagonal matrix involving innovation variances. Local polynomial smoothing estimation is proposed to model the nonpara- metric smoothing functions of the mean, generalized autoregressive coe±cients and (log) innovation variances, simultaneously. We provide theoretical justi¯cation of consistency of the ¯tted smoothing curves in the mean, generalized autoregressive parameters and (log) innovation variances. Two real data sets are analyzed for illustration. Simulation studies are made to evaluate the e±cacy of the proposed method.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||Covariance modelling; Local likelihood method; Longitudinal studies; Mod- i¯ed Cholesky decomposition; Modi¯ed cross validation with leave-one-subject-out; Non- parametric regression.|
|Subjects:||MSC 2000 > 15 Linear and multilinear algebra; matrix theory|
MSC 2000 > 62 Statistics
|Deposited By:||Ms Lucy van Russelt|
|Deposited On:||09 July 2009|