High-dimensional asymptotic behavior of the difference between the log-determinants of two Wishart matrices

Consistent Bayesian information criterion based on a mixture prior for possibly high‐dimensional multivariate linear regression models

“…To deal with both of the LS and HD asymptotic frameworks at the same time, we consider the following asymptotic framework: $$$$ n\to \infty, \kern0.60em {c}_{n,p}=\frac{p}{n}\to {c}_0\in \left[0,1\right). $$$$ This framework has been investigated in many studies, such as Yanagihara et al (2017) and Yanagihara (2019). We write the limit under () as $$$$ \underset{\begin{array}{c}n\to \infty \\ {}{c}_{n,p}\to {c}_0\end{array}}{\lim }, $$$$ and we use the notation $$$ p(n) $$$ for $$$ p $$$ when we need to emphasize that it may vary with $$$ n. $$$ Following the existing literature, we assume that $$$ p(n) $$$ is nondecreasing, and therefore, $$$ p(n) $$$ is either bounded or divergent.…”

“…This framework has been investigated in many studies, such as Yanagihara et al (2017) and Yanagihara (2019). We write the limit under (2) as…”