Revisiting the Neyman-Scott model: an Inconsistent MLE or an Ill-defined Model?

TL;DR

This paper revisits the Neyman-Scott model to argue that its inconsistency issues stem from an ill-defined model rather than the ML method itself, demonstrating that proper reformulation yields consistent estimators.

Contribution

It shows that the Neyman-Scott model's inconsistency is due to ill-definition, and a simple reformulation makes the model well-defined with consistent ML estimators.

Findings

Reformulating the model resolves inconsistency issues.

ML estimators become consistent and efficient with the reformulated model.

The core problem is the model's ill-definition, not the ML method.

Abstract

The Neyman and Scott (1948) model is widely used to demonstrate a serious weakness of the Maximum Likelihood (ML) method: it can give rise to inconsistent estimators. The primary objective of this paper is to revisit this example with a view to demonstrate that the culprit for the inconsistent estimation is not the ML method but an ill-defined statistical model. It is also shown that a simple recasting of this model renders it well-defined and the ML method gives rise to consistent and asymptotically efficient estimators.