Spiked singular values and vectors under extreme aspect ratios

Michael J. Feldman

Journal of Multivariate Analysis, 2023, vol. 196, issue C

Abstract: The behavior of the leading singular values and vectors of noisy low-rank matrices is fundamental to many statistical and scientific problems. Theoretical understanding currently derives from asymptotic analysis under one of two regimes: classical, with a fixed number of rows, large number of columns or vice versa; and proportional, with large numbers of rows and columns, proportional to one another. This paper is concerned with the disproportional regime, where the matrix is either “tall and narrow” or “short and wide”: we study sequences of matrices of size n×mn with aspect ratio n/mn→0 or n/mn→∞ as n→∞. This regime has important “big data” applications.

Keywords: Random matrix; Singular value; Singular vector; Spiked covariance; Spiked model (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2023.105187

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