Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance--Correlation Parameters

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High‐dimensional covariance matrix estimation (2019, background): “(Huang, Liu, Pourahmadi, & Liu, 2006; Lam & Fan, 2009; Ravikumar, Wainwright, Raskutti, & Yu, 2011; Rothman, Bickel, Levina, & Zhu, 2008), modified Cholesky decomposition (see (6)) with regularization (Pan & Mackenzie, 2003; Pourahmadi, 2007; Rothman, Levina, & Zhu, 2010), graphical lasso (Friedman,”
Wishart distributions for decomposable covariance graph models (2011, methodology): “This decomposition of is referred to as the modified Cholesky decomposition of (see [25]).”
Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging (2009, methodology): “For example, Cholesky decompositions are frequently used for modeling longitudinal data, both with Bayesian and random effect models [e.g., see Daniels and Kass (2001); Chen and Dunson (2003); Pourahmadi (2007)].”
MCMC Estimation of Restricted Covariance Matrices (2009, methodology): “Because of these features, the decomposition has recently been employed in maximum likelihood estimation (Pourahmadi 1999, 2000, 2007) and covariance matrix modeling through partial autocorrelations (Daniels and Pourahmadi 2008).”
Nonparametric eigenvalue-regularized precision or covariance matrix estimator (2016, background): “MSC classification : 62G20, 15B52 Key words and phrases.”