A simulation study to compare various covariance adjustment techniques

A common procedure when combining two multivariate unbiased estimates (or forecasts) is the covariance adjustment technique (CAT). Here the optimal combination weights depend on the covariance structure of the estimators. In practical applications, however, this covariance structure is hardly ever known and, thus, has to be estimated. An effect of this drawback may be that the theoretically best method is no longer the best. In a simulation study (using normally distributed data) three different variants of CAT are compared with respect to their accuracy. These variants are different in the portion of the covariance structure that is estimated. We characterize which variant is appropriate in different situations and quantify the gains and losses that occur.