Nonparametric Regression of Covariance Structures in Longitudinal Studies

Pan, Jianxin and Ye, Huajin and Li, Runze (2009) Nonparametric Regression of Covariance Structures in Longitudinal Studies. [MIMS Preprint]

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Abstract

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 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	09 Jul 2009
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1286

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