Asymptotic Optimality of Experimental Designs in Estimating a Product of Means
In nonlinear estimation problems with linear models, one difficulty in obtaining optimal designs is their dependence on the true value of the unknown parameters. A Bayesian approach is adopted with the assumption the means are independent apriori and have conjuguate prior distributions. The problem of designing an exper- iment to estimate the product of the means of two normal populations is considered. The main results determine an asymptotic lower bound for the Bayes risk, and a necessary and sufficient condition for any sequential procedure to achieve the bound.