Basak Sancharee, Basu Ayanendranath, Jones M C
Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata India.
School of Mathematics and Statistics, The Open University, Milton Keynes, UK.
J Appl Stat. 2020 Mar 13;48(3):536-556. doi: 10.1080/02664763.2020.1736524. eCollection 2021.
The density power divergence, indexed by a single tuning parameter , has proved to be a very useful tool in minimum distance inference. The family of density power divergences provides a generalized estimation scheme which includes likelihood-based procedures (represented by choice for the tuning parameter) as a special case. However, under data contamination, this scheme provides several more stable choices for model fitting and analysis (provided by positive values for the tuning parameter ). As larger values of necessarily lead to a drop in model efficiency, determining the optimal value of to provide the best compromise between model-efficiency and stability against data contamination in any real situation is a major challenge. In this paper, we provide a refinement of an existing technique with the aim of eliminating the dependence of the procedure on an initial pilot estimator. Numerical evidence is provided to demonstrate the very good performance of the method. Our technique has a general flavour, and we expect that similar tuning parameter selection algorithms will work well for other M-estimators, or any robust procedure that depends on the choice of a tuning parameter.
由单个调整参数索引的密度幂散度已被证明是最小距离推断中非常有用的工具。密度幂散度族提供了一种广义估计方案，其中包括基于似然的方法（由调整参数的特定选择表示）作为特殊情况。然而，在数据受污染的情况下，该方案为模型拟合和分析提供了几个更稳定的选择（由调整参数的正值提供）。由于较大的 值必然导致模型效率下降，在任何实际情况下确定 的最佳值以在模型效率和抗数据污染稳定性之间提供最佳折衷是一项重大挑战。在本文中，我们对现有技术进行了改进，旨在消除该过程对初始初步估计器的依赖。提供了数值证据来证明该方法的良好性能。我们的技术具有普遍适用性，并且我们预计类似的调整参数选择算法将适用于其他M估计器或任何依赖于调整参数选择的稳健过程。
