On Sufficient Conditions in the Marchenko--Pastur Theorem
Abstract
We find general sufficient conditions in the Marchenko--Pastur theorem for high-dimensional sample covariance matrices associated with random vectors, for which the weak concentration property of quadratic forms may not hold in general. The results are obtained by means of a new martingale method, which may be useful in other problems of random matrix theory.
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Published In
Theory of Probability & Its Applications
Pages: 657 - 673
ISSN (online): 1095-7219
Copyright
© 2024, Society for Industrial and Applied Mathematics.
History
Submitted: 28 June 2023
Published online: 7 February 2024
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