A note on G. R. Dolby's unreplicated ultrastructural model

It is demonstrated that maximum likelihood estimators exist for the intercept, slope and unknown error variance in Dolby's (1976) unreplicated ultrastructural model with known error variance ratio even when the ratio of the variability of the measured variables to the variability of the measurement errors is unknown. This corrects an assertion in Dolby's paper. Patefield's (1978) adjusted maximum likelihood estimators for this model are shown to be strongly consistent and jointly asymptotically normal, and also best in Fisher's sense within a broad class of asymptotically normal estimators. Finally, it is noted that Patefield's adjusted estimators are asymptotically equivalent to the maximum likelihood estimators in a certain related structural model.