Disentangle intrinsic QSO evolution from reconstruction and selection biases

Determine whether the redshift-dependent difference in the inferred QSO luminosity-relation slope arises from intrinsic QSO evolution or from kernel-reconstruction effects, boundary effects, tracer-redshift-distribution sensitivity, flux selection, or unresolved instrument/provenance mixtures.

Background

The analysis finds substantially different QSO slopes in low- and high-source-redshift subsamples, but the authors explicitly treat this separation as a calibration or reconstruction consistency diagnostic rather than as evidence for physical QSO evolution. The fixed-bandwidth Nadaraya–Watson reconstruction and the absence of object-level instrument and provenance labels prevent the analysis from identifying the origin of the redshift dependence.

The authors note that the tested bandwidth variations do not exclude shared redshift-dependent biases, including boundary effects and sensitivity to the tracer redshift distribution. Resolving the issue requires comparing alternative reconstruction methods, such as local-linear or adaptive-bandwidth estimators, and separating these effects from intrinsic evolution, selection effects, and instrument-dependent systematics.

References

However, all four tests use the same fixed-bandwidth Nadaraya--Watson estimator. They do not rule out shared redshift-dependent biases, including boundary effects and sensitivity to the tracer redshift distribution \citep{fan92}. The split is therefore a calibration/reconstruction consistency diagnostic, not a separation of smoothing bias from intrinsic QSO evolution. A comparison with local-linear or adaptive-bandwidth reconstruction would be needed to investigate estimator dependence further.

— Late-time distance consistency and model-independent curvature inference with strong lensing, quasars, and galaxy clusters  (2610.26097 - Hu et al., 19 Oct 2026) in Section 5.4, “Redshift-binned consistency of the QSO calibration” (Section \ref{sect:redshift_split})