Computation of least squares trimmed regression--an alternative to least trimmed squares regression

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.