On an additive decomposition of the BLUE in a multiple-partitioned linear model

Necessary and sufficient conditions are derived for the BLUE in a general multiple-partitioned linear model { y , X 1 β 1 + ⋯ + X k β k , σ 2 Σ } to be the sum of the BLUEs under the k small models { y , X 1 β 1 , σ 2 Σ } , … , { y , X k β k , σ 2 Σ } . Some consequences and further research topics are also given.