**Optimal Allocation for Estimating the Product of Two
Means**

Janis Hardwick

Statistics Department, University of Michigan

Quentin F. Stout

EECS Department, University of Michigan

Although selecting the form of an optimal estimator is critical to
solving this problem, the real difficulty lies in determining an optimal
strategy for sampling from the two populations. The problem of optimal
*estimation* reduces, therefore, to a problem of optimal
*allocation* which can be solved exactly using dynamic programming. We
utilize similar programming techniques to evaluate exactly some of the
other strategies that have been proposed for this problem. (The term
*exact* is used repeatedly here to stress the fact that none of the
computational results depend on simulation studies.)

**Keywords:** sequential allocation, nonlinear estimation,
dynamic programming, reliability, myopic allocation, fixed allocation

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