Why DD-Payne oxygen precision appears to beat the Cramér–Rao bound

Explain why the internal precision for oxygen abundance derived with the Data-Driven Payne from DESI Early Data Release spectra is slightly smaller than the Cramér–Rao bound, and ascertain whether covariance among labels, particularly with carbon and nitrogen, accounts for this apparent discrepancy.

Background

The authors compare internal precision of their label estimates against theoretical limits from the Cramér–Rao bound. For most elements, uncertainties are within a factor of two of the bound, but oxygen shows a slightly smaller error than the bound, which should represent a lower limit.

They explicitly state that the detailed reason for this is unclear and hypothesize that label covariance, especially among nitrogen and carbon, might play a role, leaving the phenomenon unexplained.