document: Generalized confidence sets for a statistically indeterminate random vector 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
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