**Optimal Allocation for Estimating the Mean of a
Bivariate Polynomial**

Janis Hardwick

Statistics Department, University of Michigan

Quentin F. Stout

EECS Department, University of Michigan

Using a decision theoretic approach, we seek to minimize the
Bayes risk that arises from using a squared error loss function.
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 using dynamic
programming. Similar programming techniques are utilized to
evaluate properties of a number of ad hoc allocation
strategies that might also be considered for use in this problem.
Two sample polynomials are analyzed along with a number of
examples indicating the effects of different prior parameters settings.
The effects of differences between prior parameters used in the design
and analysis stages of the experiment are also examined.

**Keywords:** nonlinear estimation, sequential design, robustness,
myopic, hyperopic, dynamic programming, adaptive allocation, product,
Bayesian, fault tolerance

Copyright © 1997, 1996. | Last modified: 4 Mar 1997 |