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Consider the $p\times p$ matrix that is the product of a populationcovariance matrix and the inverse of another population covariance matrix.Suppose that their difference has a divergent rank with respect to $p$, whentwo samples of sizes $n$ and $T$ from the two populations are available, weconstruct its corresponding sample version. In the regime of high dimensionwhere both $n$ and $T$ are proportional to $p$, we investigate the limitinglaws for extreme (spiked) eigenvalues of the sample (spiked) Fisher matrix whenthe number of spikes is divergent and these spikes are unbounded.

Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes