Confidence intervals are widely used in statistical practice as indicators of precision for related point estimators or as estimators in their own right. In the present paper it is shown that for some models, including most linear and nonlinear errors-in-variables regression models, and for certain estimation problems arising in the context of classical linear models, such as the inverse regression problem, 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.
"The Nonexistence of 100$(1 - \alpha)$% Confidence Sets of Finite Expected Diameter in Errors-in-Variables and Related Models." Ann. Statist. 15 (4) 1351 - 1362, December, 1987. https://doi.org/10.1214/aos/1176350597