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B0320
**Title: **Testing for subsphericity when $n$ and $p$ are of different asymptotic order
**Authors: **Joni Virta - University of Turku (Finland) **[presenting]**

**Abstract: **A classical test of subsphericity is extended, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional regime where the signal eigenvalues of the covariance matrix diverge to infinity and either $p/n \rightarrow 0$ or $p/n \rightarrow \infty$. In the latter case, we further require that the divergence of the eigenvalues is suitably fast in a specific sense. The developments complement earlier results in the literature that established equivalent results in the case $p/n \rightarrow \gamma \in (0, \infty)$. As a second main contribution, we use the test to derive a consistent estimator for the latent dimension of the model. Simulations and a real data example are used to demonstrate the results, also providing evidence that the test might be further extendable to a wider asymptotic regime.