Chapter 8 - Local Operator Theory, Random Matrices and Banach Spaces

By K. Davidson, S. Szarek. 2001

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CONSISTENCY OF RESTRICTED MAXIMUM LIKELIHOOD ESTIMATORS OF PRINCIPAL COMPONENTS (2008, background): “This proposition can be easily proved using an exponential inequality by Davidson and Szarek (2001) on the fluctuations of the extreme eigenvalues of a Wishart matrix.”
The sparsity and bias of the Lasso selection in high-dimensional linear regression (2008, background): “We refer to Bai (1999) and Davidson and Szarek (2001) for further discussion on random covariance matrices.”
ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL (2007, result): “Proof of Proposition 1 In order to prove this result the following result, a part of Theorem 2.13 of Davidson and Szarek (2001), is used.”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “Estimating structured high-dimensional covariance and precision matrices 15 See also Davidson and Szarek (2001) for more refined results under the Gaussian assumption.”
Confidence intervals for low dimensional parameters in high dimensional linear models (2011, background): “It follows from theorem II.13 of Davidson and Szarek (2001) that, for certain positive {δ0, δ1, δ2}, X ′n,p”