Work

Asymptotic limits of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with weak signals and heteroskedastic noise

Year: 2025

Type: article

Abstract: This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity, and that the deterministic signal has the same magnitude as the noise and can have a rank that tends to infinity. We develop the asymptotic limits of the left and right spiked singular vectors of the signal-plus-noise data matrix and the limits of the spiked eigenvalues of the corresponding Gram matrix. As an application, we propose a new criterion to estimate the number of clusters in clustering problems.

Source: Bernoulli

DOI: 10.3150/24-bej1808

Authors: Xiaoyu Liu, Yiming Liu, Guangming Pan, Lingyue Zhang, Zhixiang Zhang

Institutions: Jinan University, Nanyang Technological University, Dongbei University of Finance and Economics, University of Macau

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4409308308

FWCI: 3.342

Cites: 60

Cited by: 5

Related to: 10