The density power divergence, indexed by a single tuning parameter α, 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 α=0 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 α). As larger values of α necessarily lead to a drop in model efficiency, determining the optimal value of α 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.

中文翻译：

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关于“最佳”密度功率发散调谐参数

由单个调谐参数 α 索引的密度功率散度已被证明是最小距离推断中非常有用的工具。密度功率散度族提供了一种广义估计方案，其中包括基于似然的过程（由调谐参数的选择 α=0 表示）作为特例。然而，在数据污染的情况下，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 α 的正值提供）。由于较大的 α 值必然会导致模型效率下降，因此确定最佳 α 值以在任何实际情况下提供模型效率和稳定性之间的最佳折衷以防止数据污染是一项重大挑战。在本文中，我们提供了对现有技术的改进，目的是消除程序对初始试验估计量的依赖。提供了数值证据来证明该方法的非常好的性能。我们的技术具有一般性，我们希望类似的调整参数选择算法适用于其他 M 估计器，或任何依赖于调整参数选择的稳健程序。