This is obvious for estimators that explicitly depend on symmetry,
such as the Gastwirth and trimean estimators introduced by Koenker and Bassett (1978).
such as those used by Temple (1998) and Zaman et al. (2001),
are also sensitive to departures from the assumption of symmetric homoskedastic errors.
Simulation results for these and other estimators are presented in Baldauf and Santos Silva (2009).