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