A Deterministic Algorithm for Robust Location and Scatter
A Deterministic Algorithm for Robust Location and Scatter
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DOI：
10.1080/10618600.2012.672100
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发表时间：
2012-09-01
影响因子：
2.4
通讯作者：
Verdonck, Tim
中科院分区：
文献类型：
--
作者：
Hubert, Mia;Rousseeuw, Peter J.;Verdonck, Tim
大多数用于多变量位置和散布的高稳健估计器的算法都是从绘制大量随机子集开始的。例如，Rousseuw和Van Driessen的FASTMCD算法就是这样开始的，然后采取所谓的集中步骤来获得更准确的MCD近似值。FASTMCD算法是仿射等变的，但不是置换不变的。在本文中，我们提出了一种确定性算法，记为DetMCD，它不使用随机子集，而且速度更快。它计算少量的确定性初始估计器，然后是集中步骤。DetMCD是置换不变的，并且非常接近仿射等变。我们将其与FASTMCD以及Maronna和Zamar的OGK估计器进行了比较。我们还在真实和模拟的数据集上说明了它，以及主成分分析、分类和时间序列分析的应用。补充材料(DetMCD算法和数据集的MatLab代码)可在网上获得。
Most algorithms for highly robust estimators of multivariate location and scatter start by drawing a large number of random subsets. For instance, the FASTMCD algorithm of Rousseeuw and Van Driessen starts in this way, and then takes so-called concentration steps to obtain a more accurate approximation to the MCD. The FASTMCD algorithm is affine equivariant but not permutation invariant. In this article, we present a deterministic algorithm, denoted as DetMCD, which does not use random subsets and is even faster. It computes a small number of deterministic initial estimators, followed by concentration steps. DetMCD is permutation invariant and very close to affine equivariant. We compare it to FASTMCD and to the OGK estimator of Maronna and Zamar. We also illustrate it on real and simulated datasets, with applications involving principal component analysis, classification, and time series analysis. Supplemental material (Matlab code of the DetMCD algorithm and the datasets) is available online.