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Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 4, Pages 910–919 (Mi tvp3686)  

This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Spectral properties of sample covariance matrices

V. I. Serdobol'skii

Moscow State Institute of Electronics and Mathematics

Abstract: The expectation value of the resolvents of sample covariance matrices and the variance of their matrix elements are investigated. It is assumed only that variables have zero expectation values and the maximal fourth moment of variables exists. The principal spectral equations obtained earlier only in the form of limit formulas are derived with upper estimates of the remainder terms, accurate up to absolute constants. The remainder terms prove to be small for large sample size and a small value of a special measure of the quadratic forms variance.

Keywords: spectral functions, sample covariance matrix, multivariate analysis, increasing dimension.

Full text: PDF file (529 kB)

English version:
Theory of Probability and its Applications, 1995, 40:4, 777–786

Bibliographic databases:

Received: 16.04.1992

Citation: V. I. Serdobol'skii, “Spectral properties of sample covariance matrices”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 910–919; Theory Probab. Appl., 40:4 (1995), 777–786

Citation in format AMSBIB
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\by V.~I.~Serdobol'skii
\paper Spectral properties of sample covariance matrices
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 4
\pages 910--919
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1405159}
\zmath{https://zbmath.org/?q=an:0898.62081}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 4
\pages 777--786
\crossref{https://doi.org/10.1137/1140091}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WD22100021}


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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. V. I. Serdobol'skii, “Theory of essentially multivariate statistical analysis”, Russian Math. Surveys, 54:2 (1999), 351–379  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Serdobolskii V.I., “Matrix shrinkage of high–dimensional expectation vectors”, Journal of Multivariate Analysis, 92:2 (2005), 281–297  crossref  mathscinet  zmath  isi
    3. V. I. Serdobol'skii, “Spectra of infinite-dimensional sample covariance matrices”, Theoret. and Math. Phys., 148:2 (2006), 1135–1146  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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