Moderate Deviations for Extreme Eigenvalues of Real-Valued Sample Covariance Matrices

Hui Jiang (), Shaochen Wang () and Wang Zhou ()
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Hui Jiang: Nanjing University of Aeronautics and Astronautics
Shaochen Wang: South China University of Technology
Wang Zhou: National University of Singapore

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 791-808

Abstract: Abstract Consider the sample covariance matrices of form $$W=n^{-1}C C^{\top }$$ W = n - 1 C C ⊤ , where C is a $$k\times n$$ k × n matrix with real-valued, independent and identically distributed (i.i.d.) mean zero entries. When the squares of the i.i.d. entries have finite exponential moments, the moderate deviations for the extreme eigenvalues of W are investigated as $$n\rightarrow \infty $$ n → ∞ and either k is fixed or $$k\rightarrow \infty $$ k → ∞ with some suitable growth conditions. The moderate deviation rate function reveals that the right (left) tail of $$\lambda _{\max }$$ λ max is more like Gaussian rather than the Tracy–Widom type distribution when k goes to infinity slowly.

Keywords: Sample covariance matrices; Extreme eigenvalues; Moderate deviations; 60F10; 60B20; 60G50 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-020-00999-x

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