Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach
Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach
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DOI：
10.1080/02664763.2015.1016901
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发表时间：
2015-09-02
影响因子：
1.5
通讯作者：
Basu, Ayanendranath
中科院分区：
文献类型：
--
作者：
Ghosh, Abhik;Basu, Ayanendranath
密度功率散度（DPD）测量，定义为一个单一的参数，已被证明是一个流行的工具，在稳健估计[1]领域。最近，Ghosh和Basu[5]严格地建立了独立非齐次观测下mdpde的渐近性质。在本文中，我们提出了一个广泛的数值研究来描述该方法在线性回归情况下的性能，线性回归是在非齐次数据情况下最常见的设置。此外，我们将现有的选择最优鲁棒性调整参数的方法从独立和同分布（i.i.d）数据的情况扩展到非均匀观测的情况。正确选择调优参数对结果分析的适当性至关重要。在线性回归问题的背景下，通过对实际和模拟数据的广泛数值研究，探讨了最优鲁棒性调整参数的选择。
The density power divergence (DPD) measure, defined in terms of a single parameter , has proved to be a popular tool in the area of robust estimation [1]. Recently, Ghosh and Basu [5] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.