Generalized Cochran–Wald statistics in combining of experiments

In this paper we consider a general variance components model for combining experiments where in each experiment an estimate of the parameter of interest is given. Statistical inference on the parameter of interest can be based on weighted quadratic forms of the estimates from each experiment which can be seen as generalized Cochran–Wald statistics. Two important special cases of the general model are discussed in detail. One special case reflects the situation that no reliable information of the variance of the estimate in each experiment is given. This problem can be seen as a generalized common mean problem. The second special case deals with the fact that only a part of the variance of the estimate can be appropriately estimated in each experiment.