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    Robust estimation of the correlation matrix of longitudinal data

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    Type
    Article
    Authors
    Maadooliat, Mehdi
    Pourahmadi, Mohsen
    Huang, Jianhua Z.
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2011-09-23
    Online Publication Date
    2011-09-23
    Print Publication Date
    2013-01
    Permanent link to this record
    http://hdl.handle.net/10754/599523
    
    Metadata
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    Abstract
    We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ=DLL⊤D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D, and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t-distributions with unknown degrees of freedom. We develop a Fisher scoring algorithm for computing the maximum likelihood estimator of the parameters when the nonredundant and unconstrained entries of (L,D) are modeled parsimoniously using covariates. We compare our results with those based on the modified Cholesky decomposition of the form LD2L⊤ using simulations and a real dataset. © 2011 Springer Science+Business Media, LLC.
    Citation
    Maadooliat M, Pourahmadi M, Huang JZ (2011) Robust estimation of the correlation matrix of longitudinal data. Stat Comput 23: 17–28. Available: http://dx.doi.org/10.1007/s11222-011-9284-6.
    Sponsors
    We would like to thank an associate editor and the referees for their constructive comments, Dr. T.-I. Lin for providing us the tumor growth data. The work of the second author was partially supported by the NSF grant DMS-0906252, and that of the third was partially supported by grants from NCI (CA57030), NSF (DMS-0907170), and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    Statistics and Computing
    DOI
    10.1007/s11222-011-9284-6
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11222-011-9284-6
    Scopus Count
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