Sufficiency and completeness in the linear model

This paper provides further contributions to the theory of linear sufficiency and linear completeness. The notion of linear sufficiency was introduced by 2], 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.