The least squares of depth trimmed (LST) residuals regression, proposed in Zuo and Zuo (2023) \cite{ZZ23}, serves as a robust alternative to the classic least squares (LS) regression as well as a strong competitor to the famous least trimmed squares (LTS) regression of Rousseeuw (1984) \cite{R84}. Theoretical properties of the LST were thoroughly studied in \cite{ZZ23}. The article aims to promote the implementation and computation of the LST residuals regression for a broad group of statisticians in statistical practice and demonstrates that (i) the LST is as robust as the benchmark of robust regression, the LTS regression, and much more efficient than the latter. (ii) It can be as efficient as (or even more efficient than) the LS in the scenario with errors uncorrelated with mean zero and homoscedastic with finite variance. (iii) It can be computed as fast as (or even faster than) the LTS based on a newly proposed algorithm.

翻译：深度修剪最小二乘（LST）残差回归（Zuo与Zuo，2023）是经典最小二乘（LS）回归的一种稳健替代方法，同时也是Rousseeuw（1984）提出的著名最小修剪平方（LTS）回归的有力竞争者。Zuo与Zuo（2023）已对LST的理论性质进行了深入探讨。本文旨在推动LST残差回归在统计实践中面向广大统计学家的应用与计算，并证明：（i）LST与稳健回归的基准——LTS回归同样稳健，且效率显著高于后者；（ii）在误差与均值无关、均值为零、方差有限且同方差的情形下，LST的效率可与LS相当（甚至更高）；（iii）基于新提出的算法，LST的计算速度可与LTS相当（甚至更快）。