Best estimators in models with individually split experimental units

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The author deals with a classical split-plot design in which the effect of levels of factor A, i.e., the whole plot treatments, and the effect of levels of factor B, i.e., the split-plot treatments, on the values of some variable are investigated. He considers four different models: (i) a fixed model, i.e., the effects of both factors are fixed; (ii) two mixed models, i.e., the effects of A are random and the effects of B are fixed, or the effects of A are fixed and the effects of B are random; (iii) a random model, i.e., the effects of both factors are random. It is assumed also that block effects are always random. In all the above linear models, it is proved that, for the estimable functions of the fixed parameters, there exist uniformly best unbiased estimators. Moreover, uniformly best unbiased quadratic estimators of suitable variance components are given in the above linear models. MR0707815