Multiple recent statistical studies formally establish that quantile regression estimators possess statistical consistency and asymptotic normality under appropriate regularity conditions.
The retrieved papers consistently support the claim that quantile regression estimators achieve statistical consistency under regularity conditions. Papers [2], [3], [4], [5], and [9] explicitly establish the theoretical consistency and asymptotic properties of various quantile regression estimators (such as high-dimensional, tensor, stratified, cure model, and additive variants) under standard regularity assumptions. None of the papers refute the claim. Therefore, the balance verdict is SUPPORTED.