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

2023/10/21 by Liu, Xiaoyu, Liu, Yiming, Pan, Guangming +2 · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2310.13939

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-plusnoise 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.

Cited by

• Structural Effect and Spectral Enhancement of High-Dimensional Regularized Linear Discriminant Analysis

Related

• Asymptotic distribution of spiked eigenvalues in the large signal-plus-noise models
• On determining the number of spikes in a high-dimensional spiked population model
• Detection problems in the spiked matrix models
• Asymptotic Theory of Eigenvectors for Random Matrices With Diverging Spikes
• Asymptotic Joint Distribution of Extreme Sample Eigenvalues and Eigenvectors in the Spiked Population Model