Valid inference under Byzantine contamination

Develop valid statistical inference for heterogeneity-calibrated Byzantine-robust distributed composite quantile regression under conditions such as a sufficiently fast vanishing contamination fraction, and establish asymptotic normality at the pooled root-N_H rate when those conditions hold.

Background

The paper derives a nonasymptotic estimation and support-recovery bound whose contamination term does not vanish when the Byzantine fraction is fixed and the local sample size remains fixed. Consequently, the authors explicitly note that their results do not establish asymptotic normality at the pooled root-N_H rate under fixed positive contamination.

The unresolved direction is to formulate and prove valid inferential results under additional assumptions, potentially including a sufficiently fast vanishing Byzantine contamination fraction. Such results would extend the paper's conditional estimation theory from error bounds and support recovery to distributional approximation and confidence procedures.