Comparison of Confidence Sets Designs for Various Degrees of Knowledge

Abstract

Confidence sets are random sets constructed in such a way that the probability that they contain the estimated parameter achieves a chosen level. This paper deals with combining information from two estimates and discusses several designs with respect to various degrees of knowledge of the joint probability density function. Namely, the designs by fusion, intersection and union are considered for unknown joint density, known Gaussian joint density and Gaussian joint density with unknown cross-covariance. Evaluation criteria are proposed and the confidence sets are compared using simple numerical example.