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 a robust alternative to the classic least sum of squares (LS) 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 and asymptotically normal. Approximate algorithms for computing LST are proposed and tested in synthetic and real data examples. These experiments indicate that one of the algorithms can compute the LST estimator very fast and with relatively smaller variances than 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 high dimensional data sets (with possible contamination and outliers).
翻译:在著名的减缩方块总和(LTS)中,残留物先是平方,然后是修剪。在本篇文章中,我们首先用深度裁剪办法裁剪剩余物(LTS)(1984年),然后用其余残余物平方。可以尽量减少减缩残余物平方方块之和的估算物(LTS)(Lusseeuw(LTS)(LTS)(LTS)(LTS)(LTS)(Lusseeuew(1984年)))),用最差的平方块(LTS)(Lusseeuew(LS)(LTS)(LTS)(LTS)是典型的最小的替代物分解点,在合成和真实数据实例中,提出并测试计算LST(LS)的最接近的算法方法。这些实验表明,可以将LSTS-ST(50美元)污染最高值与LS(LST)标准相对而言,最短、最短、最接近于最接近于最接近的数据。