Non-Existence of Consistent Estimator Sequences and Unbiased Estimates: A Practical Example
It is often thought that identiﬁability implies existence of consistent estimator sequences. A rather artiﬁcial counter example is given in . We here consider a case which often arises in experimental and survey practice. The example concerns a model with intraclass correlation ρ. For ρ negative an indeﬁnitely large sequence of observations cannot arise from such a model and so the discussion of consistency is restricted to ρ > 0. For any non-degenerate range of ρ we show that no unbiased estimate exists for the variance of the mean of the observations. Certain other aspects of estimation in models of this sort are considered in .
Konijn, H. S., "Non-Existence of Consistent Estimator Sequences and Unbiased Estimates: A Practical Example" (1962). Cowles Foundation Discussion Papers. 374.