Robust estimation of the correlation matrix of longitudinal data

Statistics and Computing volume 23, pages17–28(2013)Cite this article

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 LD 2 L ⊤ using simulations and a real dataset.

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Affiliations

  1. Department of Statistics, Texas A&M University, College Station, USA

    Mehdi Maadooliat, Mohsen Pourahmadi & Jianhua Z. Huang

Authors
  1. Mehdi Maadooliat
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  2. Mohsen Pourahmadi
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  3. Jianhua Z. Huang
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Correspondence to Mehdi Maadooliat.

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Maadooliat, M., Pourahmadi, M. & Huang, J.Z. Robust estimation of the correlation matrix of longitudinal data. Stat Comput 23, 17–28 (2013). https://doi.org/10.1007/s11222-011-9284-6

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Keywords

  • Cholesky decomposition
  • Correlation modeling
  • Multivariate t
  • Robust estimation