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Elliptically contoured distributions
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  • Published: December 1987

Elliptically contoured distributions

  • Yehoram Gordon1 

Probability Theory and Related Fields volume 76, pages 429–438 (1987)Cite this article

  • 215 Accesses

  • 16 Citations

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Summary

Given two covariance matricesR andS for a given elliptically contoured distribution, we show how simple inequalities between the matrix elements imply thatE R(f)≦E S(f), e.g., whenx=(xi1,i2,...,in) is a multiindex vector and

$$f(x) = \mathop {\min }\limits_{i_1 } \mathop {\max }\limits_{i_2 } \mathop {\min }\limits_{i_3 } \max ...x_{i_{1,...,} i_n } ,$$

orf(x) is the indicator function of sets such as

$$\mathop \cap \limits_{i_1 } \mathop \cup \limits_{i_2 } \mathop \cap \limits_{i_3 } \cup ...[x_{i_{1,...,} i_n } \mathop< \limits_ = \lambda _{i_{1,...,} i_n } ]$$

of which the well known Slepian's inequality (n=1) is a special case.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technion, Israel Institute of Technology, 32000, Haifa, Israel

    Yehoram Gordon

Authors
  1. Yehoram Gordon
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Additional information

Supported in part by the Fund for the Promotion of Research at the Technion #100-621, and the K.&M. Bank Mathematics Research Fund #100-609

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Gordon, Y. Elliptically contoured distributions. Probab. Th. Rel. Fields 76, 429–438 (1987). https://doi.org/10.1007/BF00960067

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  • Received: 23 June 1986

  • Issue Date: December 1987

  • DOI: https://doi.org/10.1007/BF00960067

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Keywords

  • Covariance
  • Matrix Element
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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