Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix

By Mohsen Pourahmadi. 2000

291 citations recorded by the source corpus.

Subfields: Environmental Engineering, Plant Science

View Paper: https://www.semanticscholar.org/paper/413e6c772486bfc4d94d239766d65f837f6c661f

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Citations in the corpus

Kriging a soil variable with a simple nonstationary variance model (2009, background): “There are various other examples of studies where the variance of the random component of a linear model is modeled as a function of some covariate so as to avoid assumptions of homogeneity (e.g., Verbyla 1993; Pourahmadi 2000; Al-Rawwash and Pourahmadi 2006; Lee and Nelder 2006).”
Multivariate covariance generalized linear models (2015, methodology): “Liang and Zeger; 1986; Zeger et al.; 1988). Our approach diers from GEE in that we propose to model (˝) in terms of a linear combination of known matrices, following the ideas of Anderson (1973) and Pourahmadi (2000), i.e. h( (˝)) = ˝ 0Z 0 + + ˝ DZ D: (2) Here his the covariance link function, Z d w”
High dimensional covariance matrix estimation using a factor model (2007, unknown): “See, for example, Dempster (1972), Leonard and Hsu (1992), Chiu, Leonard and Tsui (1996), Diggle and Verbyla (1998), Pourahmadi (2000), Boik (2002), Smith and Kohn (2002), Wong, Carter and Kohn (2003), Wu and Pourahmadi (2003), Huang, Liu and Pourahmadi (2004), and Li and Gui (2005).”
Double hierarchical generalized linear models (with discussion) (2006, methodology): “In forming L.ρ/ the use of regression models was studied by Pourahmadi (2000) and Pan and MacKenzie (2003).”
Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “An algorithm for computing the MLE of the parameters (γ,λ) using the iterative Newton–Raphson algorithm with Fisher scoring is given in Pourahmadi (2000) along with the asymptotic properties of the estimators.”
Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage (2000, methodology): “The method of Pourahmadi (1999, 2000) is useful for modeling the covariance matrix for a response variable whose components have a natural ordering (e.g., from a longitudinal study), but it loses its appealing properties when the goal is to model the prior of the covariance matrix of regression…”
Model-Based Clustering (2016, methodology): “A modified Cholesky decomposition can be applied to a covariance matrix, and Pourahmadi (1999, 2000) exploits the fact that covariance matrix Σ of a random variable can be decomposed using the relation TΣT′ = D, where T is a unique unit lower triangular matrix and D is a unique 354 Model-Based…”
High Dimensional Inverse Covariance Matrix Estimation via Linear Programming (2010, methodology): “In addition to the aforementioned methods, sparse models have also been proposed for the modified Cholesky factorof the covariance matrix in a series of papers by Pourahmadi and co-authors (Pourahmadi, 1999; Pourahmadi, 2000; Wu and Pourahmadi, 2003; Huang et al., 2006).”
Time Varying Structural Vector Autoregressions and Monetary Policy (2005, unknown): “A decomposition of the variance covariance matrix resulting in (4) is common, especially in the literature considering the problem of efficiently estimating covariance matrices (see, for instance,Pinheiro and Bates(1996), Pourahmadi(1999, 2000), Smith and Kohn(2002)).”
Multilevel modelling of medical data (2002, background): “Pourahmadi [21, 22] considers similar models but restricted to a xed set of discrete occasions.”
Covariance matrix selection and estimation via penalised normal likelihood (2006, methodology): “In this section, we review the role of the modified Cholesky decomposition in the unconstrained reparametrisation of a covariance matrix and express the normal likelihood as a quadratic function of these new parameters ( Pourahmadi, 1999, 2000 ).”