Optimal minmax estimation and the development of minmax estimation error bounds

It is often desired to create an optimal estimator of some parameter θ given the observation x. However, the relationship between θ and x may depend on another parameter φ which is unknown to the processor and not of direct interest. In this case, an estimator which performs well for one value of φ may perform poorly for another value of φ. One approach to dealing with this problem is to develop an estimator whose worst case performance evaluated over some range of φ is as good as possible. Such an optimal minmax estimator is derived. The derivation of this estimator also motivates an approach to developing lower bounds on the minmax estimation error achievable by any estimator