In survey sampling, estimating the total for a finite population is a common objective. In power systems load research, as in many other survey sampling applications, the totals of several finite populations must be estimated from the same sample. While the sampling plan may be optimal for estimating one parameter, it is likely not to be optimal for estimating all parameters of interest. Thus a common strategy in such cases is to choose estimators for the other parameters of interest having minimum mean square error (mse) for the selected sampling plan.