Singular Wishart and multivariate beta distributions

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Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles (2006, background): “Actually the density of the law of the non-zero eigenvalues of this m atrix is known (see Srivastava (2003) and Diaz-G arcia and G utierrezJaim ez (1997)),so that the non-one eigenvalues ofZ havethe jointdensity 1 eZr (n1;n2) n2Y i= 1 n 1 r 1 2 i (1 i) r n 2 1 2 Y 1 i< j n2 j j ij; wherethe norm ali”
On the mean and variance of the generalized inverse of a singular Wishart matrix (2011, methodology): “Both of their results were based on the density of the singular Wishart distribution given by Srivastava [14], and neither gave moments of the distribution.”
Multivariate High-Frequency-Based Volatility (HEAVY) Models (2012, methodology): “t=1 vt; and then e H and e M will be estimated by QMLE in the second step. The asymptotics of the QML estimator in this two-step procedure is a direct application of two-step GMM estimation discussed in Newey and McFadden (1994). Dene elH;t(!H ; !M ;e H) and elM;t(!M ;e M ) to be the”
Multivariate Theory for Analyzing High Dimensional Data (2007, background): “When n p, S has a singular Wishart distribution, see Srivastava (2003) for its distribution.”