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Multilinear approximation on rectangles and the related moment problem
Author(s) -
Klein Haneveld Willem K.
Publication year - 2005
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2005.00295.x
Subject(s) - multilinear map , mathematics , kronecker delta , algebraic number , extension (predicate logic) , regular polygon , upper and lower bounds , combinatorics , multivariate random variable , vector valued function , discrete mathematics , pure mathematics , random variable , mathematical analysis , computer science , statistics , physics , geometry , quantum mechanics , programming language
The Edmundson–Madansky (E–M) inequality provides an upper bound of the expectation of a convex function of a random vector, provided the components of the random vector are stochastically independent. Frauendorfer and Kall extended the E–M inequality to the dependent case. This paper provides the natural algebraic setting for this extension. It is shown that multilinear approximation is the basic idea. The results and the calculations are simplified considerably by the use of Kronecker products. Moreover, the class of all functions for which the general E–M bound holds is characterized completely. It includes many nonconvex functions, for instance the multi‐chord‐dominated functions, which include the multiconvex functions.