Two stage design for estimating the product of means with cost in the   case of the exponential family
  We investigate the problem of estimating the product of means of independent populations from the one parameter exponential family in a Bayesian framework. We give a random design which allocates mi the number of observations from population Pi such that the Bayes risk associated with squared error loss and cost per unit observation is as small as possible. The design is shown to be asymptotically optimal. 
Zohra Benkamra, Mekki Terbeche, Mounir Tlemcani
stat.ME