Abstract
This work is devoted to the estimation of the convergence rate of the empirical spectral distribution function (ESD) of sparse sample covariance matrices in the Kolmogorov metric. We consider the case with the sparsity \(np_n \sim \log ^\alpha n\), for some \(\alpha >1\) and assume that the moments of the matrix elements satisfy the condition \({{\,\mathrm{\mathbb {E}}\,}}|X_{jk}|^{4+\delta }\le C<\infty \), for some \(\delta >0\). We also obtain approximation estimates for the Stieltjes transform in the bulk.
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Götze, F., Tikhomirov, A., Timushev, D. (2023). Rate of Convergence for Sparse Sample Covariance Matrices. In: Belomestny, D., Butucea, C., Mammen, E., Moulines, E., Reiß, M., Ulyanov, V.V. (eds) Foundations of Modern Statistics. FMS 2019. Springer Proceedings in Mathematics & Statistics, vol 425. Springer, Cham. https://doi.org/10.1007/978-3-031-30114-8_7
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