Testability and Estimability in Multivariate Linear Normal Model with Various Restrictions

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 (1977), Seely and Birkes (1980), Baksalary and Kala (1976a), Wawrzosek (1996), and Wawrzosek and Wesołowska-Janczarek (1998).

Keywords:

• Estimability criterion
• General multivariate model
• Growth curve
• Restriction on parameters
• Sum of profiles
• Testability conditions

Mathematics Subject Classification:

• Primary 62H12, 62H15
• Secondary 62F03, 62F30, 15A03