Inference for the variance estimate

Develop valid inferential procedures for the estimated constant conditional variance sigma^2 under the homoskedastic nonparametric random-design regression model studied in the paper.

Background

The paper establishes mean-squared-error upper bounds for variance estimators but does not develop confidence intervals, uncertainty quantification, or other inferential guarantees. The authors explicitly state that inference for the variance estimate remains a separate unresolved problem.

References

Data-driven adaptation to unknown smoothness and inference for the variance estimate remain separate problems.

— Improved Variance Estimation in Homoskedastic Nonparametric Random-Design Regression via a Two-Scale Approach  (2609.08783 - Dobriban et al., 8 Sep 2026) in Discussion section