Probability Theory and Related Fields

, Volume 76, Issue 4, pp 429–438

Elliptically contoured distributions

  • Yehoram Gordon

DOI: 10.1007/BF00960067

Cite this article as:
Gordon, Y. Probab. Th. Rel. Fields (1987) 76: 429. doi:10.1007/BF00960067


Given two covariance matricesR andS for a given elliptically contoured distribution, we show how simple inequalities between the matrix elements imply thatER(f)≦ES(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.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Yehoram Gordon
    • 1
  1. 1.Department of Mathematics, TechnionIsrael Institute of TechnologyHaifaIsrael