Minimum hellinger distance estimation with inlier modification
Minimum hellinger distance estimation with inlier modification
复制标题
带内点修正的最小 Hellinger 距离估计
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
A. Basu
中科院分区：
文献类型：
--
作者：
Rohit Patra;A. Mandal;A. Basu
对于统计学家来说，基于Hellinger距离的推理过程为基于可能性的方法提供了有吸引力的替代方案。最小Hellinger距离估计量在模型下具有完全渐近效率，在模型错误指定下具有较强的稳健性。然而，Hellinger距离对内部样本的权重太大，这似乎是该方法在小样本中效率较低的主要原因。这里对Hellinger距离的Inlier部分进行了一些修改，从而大大改善了估计量的小样本性质。修正的发散度是一般差异类的成员，并且满足必要的正则性条件，因此所得到的估计量的渐近性质遵循标准理论。在有限的仿真中，所提出的估计器在模型上表现出更好的小样本性能，并且相对于普通的最小Hellinger距离估计器具有更好的稳健性。由于改进的估计量的渐近效率与普通估计量的渐近效率相同，新的方法有望成为应用统计学家和数据分析师的有用工具。AMS(2000)学科分类。初级62F10、62F35；次级：62F12。
Inference procedures based on the Hellinger distance provide attractive alternatives to likelihood based methods for the statistician. The minimum Hellinger distance estimator has full asymptotic efficiency under the model together with strong robustness properties under model misspecification. However, the Hellinger distance puts too large a weight on the inliers which appears to be the main reason for the poor efficiency of the method in small samples. Here some modifications to the inlier part of the Hellinger distance are provided which lead to substantial improvements in the small sample properties of the estimators. The modified divergences are members of the general class of disparities and satisfy the necessary regularity conditions so that the asymptotic properties of the resulting estimators follow from standard theory. In limited simulations the proposed estimators exhibit better small sample performance at the model and competitive robustness properties in relation to the ordinary minimum Hellinger distance estimator. As the asymptotic efficiencies of the modified estimators are the same as that of the ordinary estimator, the new procedures are expected to be useful tools for applied statisticians and data analysts. AMS (2000) subject classification. Primary 62F10, 62F35; Secondary: 62F12.