To weight, or not to weight

Generalized least squares (weighted statistical analysis) has been proposed for several data analysis problems in safeguards work with the purpose of minimizing the variances of estimates. Examples are weighted regression for calibration of NDA instruments, weighted estimates for characterizing NDA working standards, and weighted analyses for sequences of MUF values. When considering the use of weighted analyses one should consider the rarely mentioned problem of how well the weights are known. If incorrect weights are chosen or if the weights are random variables, then the variance of the weighted estimate may be larger than the variance of an unweighted estimate. This paper indicates the problem by presenting results for the simplest case of averaging two independent sample means. Results of a study of averages of k>2 sample means are cited. A bibliography covering more complicated situations is presented here. For some values of the sample size and variance parameters it is known that unweighted estimates have smaller variances than weighted estimates when the weights are random variables. For other values of the parameters the reduction in the variance over unweighted estimates is very small. The difficulty in obtaining correct weights, the small gain achieved in some cases, and the additional complexity involved in estimating variances of weighted estimates suggest that the simpler unweighted estimates should often be preferred. (author)