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Original Articles

Testability and Estimability in Multivariate Linear Normal Model with Various Restrictions

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Pages 828-841 | Received 31 Mar 2006, Accepted 18 Jun 2008, Published online: 24 Mar 2009
 

Abstract

In the multivariate linear normal model, definitions and interpretations are presented for many various following types:

  • 1) restrictions on parameters O s , <p > s = 1,…, 6,

  • 2) hypotheses about parameters ,

  • 3) parametric functions C l , <p > l = 1,…, 5.

In the multivariate linear normal with the restrictive condition O s (or without this condition), the definition of testability of the any null hypothesis and estimability of parametric function C l are given. Also, equivalent conditions and necessary conditions for testability and estimability in this model are presented. The results of this work are a generalization of the results achieved by Seely (Citation1977), Seely and Birkes (Citation1980), Baksalary and Kala (Citation1976a), Wawrzosek (Citation1996), and Wawrzosek and Wesołowska-Janczarek (Citation1998).

Mathematics Subject Classification:

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