In the famous least sum of trimmed squares (LTS) of residuals estimator (Rousseeuw (1984)), residuals are first squared and then trimmed. In this article, we first trim residuals - using a depth trimming scheme - and then square the rest of residuals. The estimator that can minimize the sum of squares of the trimmed residuals, is called an LST estimator. It turns out that LST is also a robust alternative to the classic least sum of squares (LS) of residuals estimator. Indeed, it has a very high finite sample breakdown point and can resist, asymptotically, up to 50% contamination without breakdown - in sharp contrast to the 0% of the LS estimator. The population version of LST is Fisher consistent, and the sample version is strong and root-n consistent under some conditions. Three approximate algorithms for computing LST are proposed and tested in synthetic and real data examples. These experiments indicate that two of the algorithms can compute the LST estimator very fast and with relatively smaller variances, compared with that of the famous LTS estimator. All the evidence suggests that LST deserves to be a robust alternative to the LS estimator and is feasible in practice for large data sets (with possible contamination and outliers) in high dimensions.

翻译：在著名的减缩方块总和(LTS)中,残留物首先对齐,然后对齐。在本篇文章中,我们首先用深度裁剪办法对残留物进行剪裁,然后将其余的残余物平成平。可以尽量减少减缩残余物平方方方块之和的估算物称为 LST 估测器。结果显示,LST 也是典型的最小残余物平方块(LS)的最强替代物。事实上,它有一个非常有限的样本分解点,并且可以不折不扣地抵制高达50%的污染,与LS 估测器的0%形成鲜明的对比。LST 的人口版本与Fisheral一致, 样本版本在某些条件下是坚固和根性的。计算 LST 的三种大致算法都是在合成和真实数据示例中提出和测试的。这些实验表明,两种算法可以将LST 估测算器的精度与非常快速且具有相对小的替代物分解度数据相比,所有替代物的偏差都比高。