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 nn whereas the dimension pp of the observations is kept small. In this paper, we consider the case of high dimension, where pp is large compared to nn. 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.