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Generalized Confidence Sets for a Statistically Indeterminate Random Vector

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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 up 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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  1. Ural State Academy of Railway Transport, Yekaterinburg, Russia

    G. A. Timofeeva

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  1. G. A. Timofeeva
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Timofeeva, G.A. Generalized Confidence Sets for a Statistically Indeterminate Random Vector. Automation and Remote Control 63, 906–918 (2002). https://doi.org/10.1023/A:1016165621974

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