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The nonexistence of $100(1-\alpha)\%$ confidence sets of finite expected diameter in errors-in-variables and related models. (English) Zbl 0638.62035
It is shown that for some models it is impossible to construct confidence intervals for key parameters which have both positive confidence and finite expected length. The results are generalized to cover general confidence sets for both scalar and vector parameters. After proving the main theorems, models are presented such as linear and nonlinear error-in-variables regression models, and the inverse regression problem. A version of the assertion (proven as well) is that all confidence intervals with positive confidence span the whole range of the finite parameter, such as the mixing parameter in a mixed family of density functions or the location parameter of the von Mises distribution on the circle.
Reviewer: J.Tank√≥

62F25Parametric tolerance and confidence regions
62G15Nonparametric tolerance and confidence regions
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