  Estimating the number of spikes in a spiked model is an important problem in
many areas such as signal processing. Most of the classical approaches assume a
large sample size $n$ whereas the dimension $p$ of the observations is kept
small. In this paper, we consider the case of high dimension, where $p$ is
large compared to $n$. The approach is based on recent results of random matrix
theory. We extend our previous results to a more difficult situation where some
spikes are equal, and compare our algorithm to an existing benchmark method.
