Sufficiency and completeness in the linear model

AbstractThis paper provides further contributions to the theory of linear sufficiency and linear completeness. The notion of linear sufficiency was introduced by Baksalary and Kala (1981, Ann. Statist. 9, 913–916) and Drygas (in press, Sankhya) with respect to the linear model Ey = Xβ, var y = V. In addition to correcting an inadequate proof of [8], the relationship to an earlier definition and to the theory of linear prediction is also demonstrated. Moreover, the notion is extended to the model Ey = Xβ, var y = δ2V. Its connection with sufficiency under normality is investigated. An example illustrates the results