Interval Estimation in Structural Errors-in-Variables Model with Partial Replication

Confidence sets are constructed for the coefficients in a structural errors-invariables model with partial replication. These confidence sets are different from the traditional asymptotic confidence sets which have zero confidence levels, where the confidence level of a confidence set is defined to be the infimum coverage probability over the parameter space. The proposed confidence sets have positive confidence levels. Furthermore, it is shown that they have coverage probabilities converging to the nominal levels uniformly in all parameters as the sample size goes to infinity. An optimality property of the proposed confidence set for the slope in the model is also demonstrated.