A note on optimal parameter estimation under zero-excess assumptions

In the Bühlmann-Straub credibility model, optimal estimators (in the sense of minimum variance) for the variance parameters were proposed by De Vylder and Goovaerts [Insurance: Mathematics and Economics 11 (1992) 167–171] under zero excess assumptions for the involved random variables. For some results, supplementary restrictive conditions were needed. Using the variance components approach to the model, we show that one of these supplementary conditions can be dropped.