Estimation of the Number of Spikes, Possibly Equal, in the High-Dimensional Case

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.