Optimization of Interval Estimators via Invariant Embedding Technique

In the present paper, for optimization of interval estimators, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. The aim of the paper is to show how the invariance principle may be employed in the particular case of finding the interval estimators that are uniformly best invariant. The technique proposed here is a special case of more general considerations applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. This technique may be used for constructing the minimum risk estimators of state of computing anticipatory systems. To illustrate the proposed technique, examples are given.