IS r* LINEAR IN r?

Abstract

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