Existence and nonexistence theorems of finite diameter sequential confidence regions for errors-in-variables models

In errors-in-variables models, confidence sets (or intervals) for the key parameters with finite diameter and with asymptotic coverage probabilities greater than some nominal level 1 - [alpha] have been constructed. Do these sets have good coverage probabilities for any fixed sample size? The answer may be no! In fact, in these models, any finite diameter confidence sets have zero minimum coverage probability, no matter how large the sample size is as long as it is fixed. (See Gleser and Hwang (1987).) The results apply to various models, including most linear and nonlinear errors-in-variables and inverse regression problems. Sequential approach appears to lie in between fixed-sample and asymptotic approaches. It seems to be interesting to investigate whether it is possible to construct good sequential confidence sets. In the paper, we focus on the errors-in-variables models and show that the answer is negative for K-stage, for any finite positive interger K, sequential sampling. However the answer is positive for fully sequential sampling.