Elliptically contoured distributions (Q1087214)

Given two covariance matrices R and S for a given elliptically contoured distribution, we show how simple inequalities between the matrix elements imply that \(E_ R(f)\leq E_ S(f)\), e.g., when \(x=(x_{i_ 1,i_ 2,...,i_ n})\) is a multiindex vector and \[ f(x)=\min _{i_ 1}\max _{i_ 2}\min _{i_ 3}\quad \max \quad...x_{i_ 1,...,i_ n}, \] or f(x) is the indicator function of sets such as \[ \cap _{i_ 1}\cup _{i_ 2}\cap _{i_ 3}\cup...[x_{i_ 1,...,i_ n}\leq \lambda _{i_ 1,...,i_ n}] \] of which the well known Slepian's inequality \((n=1)\) is a special case.