The quantity was introduced by Barndorff-Nielsen, in part as a distributional
refinement of the signed likelihood root , a refinement that can
also be approximated by a mean and standard deviation adjustment of the root
. We clarify: that is not linear in ; that achieves large distributional
improvement on ; and that provides the definitive separation of inference
information concerning scalar component parameters of a statistical model.
These distributional and inference properties deserve broader awareness.