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Inequalities associated with intra–inter-class correlation matrices

✍ Scribed by Hiroshi Kurata

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
199 KB
Volume
88
Category
Article
ISSN
0047-259X

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✦ Synopsis

This paper complements the results of Tong (Ann. Statist. 17 (1989) 429), Shaked and Tong (Ann. Statist. 20 (1992) 614) and Eaton (in: Stochastic Inequalities, IMS Lecture Notes Monograph Series, Vol. 22, 1993, 76) by deriving some monotonicity results associated with intra-inter-class correlation matrices. In Section 2, we consider the problem of comparing these matrices in terms of the orderings induced by several subgroups of the orthogonal group. Section 3 is devoted to deriving some probability inequalities for normal random variables whose correlation matrix is of the intra-inter-class correlation structure.

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✍ R.W. Goldbach; H.L. Claasen 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 136 KB

In this paper we determine all symmetric and non-symmetric 3-class association schemes such that for their adjacency matrices D i we have Hadamard matrix of order 16 (i.e. an Hadamard matrix consisting of 16 square blocks H i j of order 4 such that H ii = J 4 and H i j J 4 = J 4 H i j = 0). It appe