Generating random correlation matrices based on partial correlations

By Harry Joe. 2006

234 citations recorded by the source corpus.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/faf9dd2bd68707c5615ff8b64dfd60351227b42b

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “…determinantal identity, |Σ|= ( p ∏ i=1 σii ) p ∏ i=2 i−j ∏ j=1 (1− π2ij),(25) has been redicovered recently by Dégerine and Lambert-Lacroix (2003), Kurowicka and Cooke (2003) and Joe (2006), but its origin can be traced to a notable and somewhat neglected paper of Yule (1907), equation (25).”
Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence (2010, unknown): “This extends the approaches suggested by Joe (2006) and Daniels and Pourahmadi (2009) for modeling covariance matrices for Gaussian data, and we show that this is an effective strategy for a range of copula functions in our empirical work.”
Pair-Copula Constructions of Multivariate Copulas (2010, background): “Random generation of correlation matrices are considered in [33] using D-vines and more general using regular vines in [42].”
Total positivity in Markov structures (2015, methodology): “We uniformly sample correlation matrices using the method suggested by Joe [18], which is implemented in the R package clusterGeneration.”
Estimating logit models with small samples (2021, unknown): “(5) Choose a covariance matrix S for the explanatory variables randomly using the method developed by Joe (2006) such that the variances along the diagonal range from 0.25 to 2.”
Covariance Matrix Estimation under Total Positivity for Portfolio Selection* (2019, methodology): “This is quite remarkable, since uniformly sampling correlation matrices, e.g. using the method described in [Joe06], shows that less than 0 .”
Multiple imputation for continuous variables using a Bayesian principal component analysis† (2014, methodology): “w dimensional structure of the data is less obvious. Instead of generating the data sets using covariance matrices with a two block diagonal structure, we generate covariance matrices at random as in [32]. More precisely, the draw is uniform over the space of positive deﬁnite correlation matrices. T”
A method for generating realistic correlation matrices (2011, background): “Although there 9 has been additional work expanding the ideas associated with generating random cor10 relation matrices [8, 16, 21, 28, 35] and even randomly generating correlation matrices 11 within particular settings [15, 33], to our knowledge there is no literature devoted to 12 the problem of a”
PLS' Janus Face – Response to Professor Rigdon's ‘Rethinking Partial Least Squares Modeling: In Praise of Simple Methods’ (2014, methodology): “…gives the undistorted, true picture: what we would get with the latent variables instead of with the proxies; R2 is uniformly distributed 1I used H. Joe (2006) to generate a million correlations, uniformly from the ellipsoid that describes all permissible correlations (the ensuing correlation…”