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Dependent Gaussian samples: Dimension-free estimation of the scatter

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Abstract

We suggest a dimension-free estimate, exact in order, of the scatter of samples chosen according to an arbitrary centered Gaussian distribution γ. This estimate involves only the spectral radius of the covariance quadratic form of γ. Bibliography: 5 titles.

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References

  1. A. V. Sudakov, V. N. Sudakov, and H. V. Weizsaecker, “Typical distributions: infinite-dimensional approaches,” in: Asymptotic Methods in Probability and Statistics with Applications, Birkhäuser (2001), pp. 205–214.

  2. V. Sudakov, “Gaussian measures. A brief survey,” Rend. Istit. Mat. Univ. Trieste, 26,Suppl., 289–325 (1994).

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  3. V. N. Sudakov and B. S. Tsirelson, “Extremal properties of half-spaces for spherically invariant measures,” Zap. Nauchn. Semin. LOMI, 41, 14–24 (1974).

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  4. B. S. Cirelson, I. A. Ibragimov, and V. N. Sudakov, “Norms of Gaussian sample functions,” Lect. Notes Math., 550, 20–41 (1976).

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  5. B. S. Tsirelson, Conjecture, Manuscript, Archives of the Laboratory of Statistical Methods, St. Petersburg Department of Steklov Institute of Mathematics.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    V. N. Sudakov & A. V. Sudakov

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  1. V. N. Sudakov
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  2. A. V. Sudakov
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 166–173.

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Sudakov, V.N., Sudakov, A.V. Dependent Gaussian samples: Dimension-free estimation of the scatter. J Math Sci 137, 4571–4574 (2006). https://doi.org/10.1007/s10958-006-0253-0

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  • DOI: https://doi.org/10.1007/s10958-006-0253-0

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