title: Generalized confidence sets for a statistically indeterminate random vector
abstract: A problem is considered for the construction of confidence sets for a random vector, the information on distribution parameters of which is incomplete. To obtain exact estimates and a detailed analysis of the problem, the notion is introduced of a generalized confidence set for a statistically indeterminate random vector. Properties of generalized confidence sets are studied. It is shown that the standard method of estimation, which relies on the unification of confidence sets, leads in many cases to wider confidence estimates. For a normally distributed random vector with an inaccurately known mean value, generalized confidence sets are built tip and the dependence of sizes of a generalized confidence set on the forms and parameters of a set of possible mean values is examined
keyphrases: generalized confidence sets statistically indeterminate random vector distribution parameters normally distributed random vector