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A limit theorem for the eigenvalues of product of two random matrices. (English) Zbl 0553.62018
If $A\sb p$ is a $p\times p$ matrix with real eigenvalues, and $pF\sb p(x)$ is the number of eigenvalues less than or equal to x, then we call $F\sb p(x)$ the spectral distribution function of $A\sb p$. Let $W\sb p=X\sb pX\sp T\sb p$ be a Wishart matrix where $X\sb p$ is $p\times m$ dimensional. Let $T\sb p$ be a $p\times p$ symmetric matrix of random variables. Under certain conditions the authors prove that if $F\sb p$ is the spectral distribution function of $m\sp{-1}W\sb pT\sb p$, then there exists a distribution function F such that $F\sb p(x)$ converges in probability to $F(x)$, for any x, as p increases without limit.
Reviewer: K.S.Miller

62E20Asymptotic distribution theory in statistics
62H10Multivariate distributions of statistics
Full Text: DOI
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