论文标题
修剪残差回归的平方最少
Least sum of squares of trimmed residuals regression
论文作者
论文摘要
在著名的残留估计量（Rousseeuw（1984））的著名修剪正方形（LT）中，残留物首先是正方形然后修剪的。在本文中，我们首先使用深度修剪方案进行修剪残差 - 然后将其余的残差平衡。可以最大程度地减少修剪残差的正方形之和的估计器称为LST估计器。 事实证明，LST是经典最小平方（LS）估算器的强大替代品。的确，它具有很高的有限样本分解点，并且可以渐近地抵抗$ 50 \％$污染而无需分解 - 与LS估算器的$ 0 \％$形成鲜明对比。 LST的总体版本是Fisher的一致性，样品版本强大且根本$ n $一致且渐近地正常。 提出了用于计算LST的近似算法，并在合成和真实数据示例中进行了测试。这些实验表明，其中一种算法可以非常快地计算LST估计量，并且比著名的LTS估计量相对较小。所有证据都表明，LST应该是LS估计器的强大替代方案，并且在实践中对于高维数据集（可能具有污染和异常值）是可行的。
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).
