Robust estimation of the correlation matrix of longitudinal data

Handle URI:
http://hdl.handle.net/10754/599523
Title:
Robust estimation of the correlation matrix of longitudinal data
Authors:
Maadooliat, Mehdi; Pourahmadi, Mohsen; Huang, Jianhua Z.
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.
Publisher:
Springer Nature
Journal:
Statistics and Computing
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
23-Sep-2011
DOI:
10.1007/s11222-011-9284-6
Type:
Article
ISSN:
0960-3174; 1573-1375
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).
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Full metadata record

DC FieldValue Language
dc.contributor.authorMaadooliat, Mehdien
dc.contributor.authorPourahmadi, Mohsenen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-28T05:52:44Zen
dc.date.available2016-02-28T05:52:44Zen
dc.date.issued2011-09-23en
dc.identifier.citationMaadooliat 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.en
dc.identifier.issn0960-3174en
dc.identifier.issn1573-1375en
dc.identifier.doi10.1007/s11222-011-9284-6en
dc.identifier.urihttp://hdl.handle.net/10754/599523en
dc.description.abstractWe 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.en
dc.description.sponsorshipWe 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).en
dc.publisherSpringer Natureen
dc.subjectCholesky decompositionen
dc.subjectCorrelation modelingen
dc.subjectMultivariate ten
dc.subjectRobust estimationen
dc.titleRobust estimation of the correlation matrix of longitudinal dataen
dc.typeArticleen
dc.identifier.journalStatistics and Computingen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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