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Teor. Veroyatnost. i Primenen., 2009, Volume 54, Issue 1, Pages 202–213 (Mi tvp2556)  

This article is cited in 5 scientific papers (total in 5 papers)

The Rate of Convergence of Spectra of Sample Covariance Matrices

F. Götze, A. N. Tikhomirov

Bielefeld University

Abstract: It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix $p^{-1}XX^T$, where $X$ is an $n\times p$ matrix with independent entries and the distribution function of the Marchenko–Pastur law is of order $O(n^{-1/2})$. The bounds hold uniformly for any $p$, including $p/n$ equal or close to $1$.

Keywords: sample covariance matrix, Marchenko–Pastur distribution, spectral distribution function

DOI: https://doi.org/10.4213/tvp2556

Full text: PDF file (165 kB)
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English version:
Theory of Probability and its Applications, 2010, 54:1, 129–140

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Received: 25.08.2008
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Citation: F. Götze, A. N. Tikhomirov, “The Rate of Convergence of Spectra of Sample Covariance Matrices”, Teor. Veroyatnost. i Primenen., 54:1 (2009), 202–213; Theory Probab. Appl., 54:1 (2010), 129–140

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bai Zh., Hu J., Zhou W., “Convergence rates to the Marchenko-Pastur type distribution”, Stochastic Process. Appl., 122:1 (2012), 68–92  crossref  mathscinet  zmath  isi  elib  scopus
    2. Li H., Bai Zh., “Convergence Rates of Spectral Distributions of Large Dimensional Quaternion Sample Covariance Matrices”, J. Korean Stat. Soc., 44:1 (2015), 28–44  crossref  mathscinet  zmath  isi  scopus
    3. Chen Yu., Goldsmith A.J., Eldar Y.C., “Backing Off From Infinity: Performance Bounds Via Concentration of Spectral Measure For Random Mimo Channels”, IEEE Trans. Inf. Theory, 61:1 (2015), 366–387  crossref  mathscinet  zmath  isi  scopus
    4. Moon H.R., Weidner M., “Linear Regression For Panel With Unknown Number of Factors as Interactive Fixed Effects”, Econometrica, 83:4 (2015), 1543–1579  crossref  mathscinet  isi  elib  scopus
    5. Bose A., Bhattacharjee M., “Kernel Density Estimates in a Non-Standard Situation”, J. Stat. Theory Pract., 15:1 (2021), 22  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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