Question: The minimum ????-quantile regression estimator is defined for ???? (0, 1) as the value of ???? minimizing the ????quantile of |y x ????|.

The minimum ????-quantile regression estimator is defined for ???? ∈ (0, 1) as the value of ???? minimizing the ????−quantile of |y − x′

????|. Show that this estimator is an S-estimator for the scale given by ????(u) = I(|u| > 1) and ???? = (1 − ????). Find its asymptotic breakdown point.

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