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- W2612206178 abstract "We study the behavior of a real $p$-dimensional Wishart random matrix with $n$ degrees of freedom when $n,prightarrowinfty$ but $p/nrightarrow 0$. We establish the existence of phase transitions when $p$ grows at the order $n^{(K+1)/(K+3)}$ for every $kinmathbb{N}$, and derive expressions for approximating densities between every two phase transitions. To do this, we make use of a novel tool we call the G-transform of a distribution, which is closely related to the characteristic function. We also derive an extension of the $t$-distribution to the real symmetric matrices, which naturally appears as the conjugate distribution to the Wishart under a G-transformation, and show its empirical spectral distribution obeys a semicircle law when $p/nrightarrow 0$. Finally, we discuss how the phase transitions of the Wishart distribution might originate from changes in rates of convergence of symmetric $t$ statistics." @default.
- W2612206178 created "2017-05-19" @default.
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- W2612206178 date "2017-05-09" @default.
- W2612206178 modified "2023-09-27" @default.
- W2612206178 title "The middle-scale asymptotics of Wishart matrices" @default.
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