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

TL;DR

This paper addresses the challenge of estimating the number of spikes in high-dimensional models where the observation dimension exceeds the sample size, extending previous methods to cases with equal spikes using random matrix theory.

Contribution

It introduces an extended algorithm for spike estimation in high-dimensional settings with equal spikes, improving upon prior approaches and comparing favorably to benchmarks.

Findings

The proposed method effectively estimates the number of spikes in high-dimensional data.

The algorithm performs well even when some spikes are equal.

Comparison shows advantages over existing benchmark methods.

Abstract

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.