Robust and efficient estimation of multivariate scatter and location
Robust and efficient estimation of multivariate scatter and location
复制标题
稳健且高效的多元散布和位置估计
DOI：
10.1016/j.csda.2016.11.006
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
V. Yohai
中科院分区：
文献类型：
--
作者：
R. Maronna;V. Yohai
研究了多变量位置和离散度的几种等变估计，它们具有很强的稳健性，有限样本效率可控，并且在大维度上是计算可行的。在这方面，使用最频繁的估计者并不十分令人满意。众所周知，最小体积椭球(MVE)和最小协方差(MCD)估计器的效率很低。S-估计量具有像双二次方这样的单调权函数，当维数p较小时效率很低，并且随着p的增加其效率趋于一个。不幸的是，对于大p的稳健性的严重损失盖过了这一优势。本文研究了四类具有可控效率的估计量，它们对中到大p的性能迄今尚未被探索：具有非单调权函数的S-估计量、MM-估计量、τ-估计量和Stahel-Donoho估计量。使用了两种类型的起始估计器：通过二次采样计算的MVE，以及先前提出的基于具有最大和最小峰度的投影的半确定性异常检测过程。模拟研究表明，对于p&≥15，具有非单调权函数的S估计可以同时达到高效率和高稳健性，而对于p<；15，可以推荐具有特定权函数的MM估计。对于这两种推荐估计，初始值都是由上述半确定性过程给出的。
Several equivariant estimators of multivariate location and scatter are studied, which are highly robust, have a controllable finite-sample efficiency and are computationally feasible in large dimensions. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and the Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-estimators with a monotonic weight function like the bisquare have a low efficiency when the dimension p is small, and their efficiency tends to one with increasing p. Unfortunately, this advantage is outweighed by a serious loss in robustness for large p. Four families of estimators with controllable efficiencies whose performance for moderate to large p has not been explored to date are studied: S-estimators with a non-monotonic weight function, MM-estimators, τ-estimators, and the Stahel–Donoho estimator. Two types of starting estimators are employed: the MVE computed through subsampling, and a semi-deterministic procedure previously proposed for outlier detection, based on the projections with maximum and minimum kurtosis. A simulation study shows that an S-estimator with non-monotonic weight function can simultaneously attain high efficiency and high robustness for p≥ 15, while an MM-estimator with a particular weight function can be recommended for p< 15. For both recommended estimators, the initial values are given by the semi-deterministic procedure mentioned above.