Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 1, Pages 15-25
doi:10.1155/S104895339000003X
Asymptotic optimality of experimental designs in estimating a product of means
Department of Applied Mathematics, Florida institute of Technology, Melbourne 32905, FL, USA
Received 1 April 1989; Revised 1 December 1989
Copyright © 1990 Kamel Rekab. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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 experiment 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.