Robust parameter estimation with a small bias against heavy contamination
Robust parameter estimation with a small bias against heavy contamination
复制标题
DOI：
10.1016/j.jmva.2008.02.004
复制
发表时间：
2008-10-01
影响因子：
1.6
通讯作者：
Eguchi, Shinto
中科院分区：
文献类型：
--
作者：
Fujisawa, Hironori;Eguchi, Shinto
在本文中，我们考虑基于一定交叉熵和散度的鲁棒参数估计。鲁棒估计被定义为经验估计的交叉熵的最小值。结果表明，从基于散度的毕达哥拉斯关系的角度来看，鲁棒估计可以被视为一种投影。这一特性意味着即使在严重污染的情况下，由异常值引起的偏差也可以变得足够小。可以看出，鲁棒估计量的渐近方差自然会与污染比率成比例地超重。人们可能推测另一种形式的交叉熵可以呈现与上面讨论的相同的行为。在某些条件下可以证明，除了这里考虑的交叉熵及其单调变换之外，没有任何交叉熵可以呈现相同的行为。 (C) 2008 Elsevier Inc. 保留所有权利。
In this paper we consider robust parameter estimation based on a certain cross entropy and divergence. The robust estimate is defined as the minimizer of the empirically estimated cross entropy. It is shown that the robust estimate can be regarded as a kind of projection from the viewpoint of a Pythagorean relation based on the divergence. This property implies that the bias caused by outliers can become sufficiently small even in the case of heavy contamination. It is seen that the asymptotic variance of the robust estimator is naturally overweighted in proportion to the ratio of contamination. One may surmise that another form of cross entropy can present the same behavior as that discussed above. It can be proved under some conditions that no cross entropy can present the same behavior except for the cross entropy considered here and its monotone transformation. (C) 2008 Elsevier Inc. All rights reserved.