Combining estimators from variety trials that are connected by control varieties only

At one site and year often numerous variety trials are performed. Sometimes these trials only have a small number of control varieties in common. It is possible to obtain best linear unbiased estimators (BLUEs) of estimable linear combinations of the variety parameters without analysing the joint observations of all trials as a whole. The unbiased local estimator of the contrast between the parameter of a new variety and the average of the parameters of the control varieties, calculated at a single trial, can be improved to the BLUE with information from the other trials. This improvement represents a contrast of contrasts between control variety parameters at the various trials. In some situations the local estimator is already the BLUE, e.g. if only one control variety is used or in case of variance-balanced designs.