On one way to choose a compromise in a family of conditionally optimal estimators
Abstract
The work is devoted to the development of stable estimation theory by A. M. Shurygin in terms of a locally stable approach based on the analysis of the indicator of estimation instability ( L-2-norm of the influence function). Within the framework of this approach, a family of conditionally optimal estimators is considered, which can be defined as optimizing the asymptotic dispersion under a constraint on instability. In practice, there may be a question of a reasonable choice of one estimator from a family that provides a compromise between the criteria defining the family. To solve the problem, it is proposed to form a functional, which is a convex linear combination of the initial criteria are normalized in such a way that the center of the family corresponds to the solution of the maximin problem regarding the arguments of the functional. It is shown that the found estimator minimizes the product of the criteria.
