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
orf(x) is the indicator function of sets such as
of which the well known Slepian's inequality (n=1) is a special case.
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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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DOI: https://doi.org/10.1007/BF00960067