Convergence and asymptotic freeness of missing data matrices

2025/08/14 by Adhikari, Kartick, Ahir, Dev
#60F99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.10610

Abstract

We consider a random matrix of the form D_n \odot X_n (known as a variance profile matrix), where \odot denotes the Hadamard product of the two matrices, D_n is a deterministic matrix, and X_n is a random matrix. We call D_n\odot X_n as a missing data matrix of X_n when the entries of D_n are either 0 or 1. This framework is commonly used in various applied fields, such as biology, neuroscience, and network data analysis. We study the convergence and asymptotic freeness of missing data matrices of iid, elliptic, and covariance random matrices. Specifically, it is known that independent iid, elliptic, and covariance matrices converge to freely independent circular, elliptic, and Marčenko-Pastur variables, respectively. In this article, we provide the necessary and sufficient conditions on deterministic matrices D_n for which these results hold true for independent missing data matrices of these three types of random matrices.

Citations

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• Freeness over the diagonal and outliers detection in deformed random\n matrices with a variance profile
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Related

• Spectral analysis of high-dimensional sample covariance matrices with missing observations
• Tests of Missing Completely At Random based on sample covariance matrices
• Concentration of measure bounds for matrix-variate data with missing values
• Freeness over the diagonal and outliers detection in deformed random\n matrices with a variance profile
• Asymptotic Freeness for Rectangular Random Matrices and Large Deviations\n for Sample Covariance Matrices With Sub-Gaussian Tails