论文标题
至少布雷格曼发散推理
On minimum Bregman divergence inference
论文作者
论文摘要
在本文中，提出了一个基于布雷格曼差异的最小差异估计量的新系列。流行的密度功率差异（DPD）类别的估计量是Bregman差异的子类。我们提出并研究了一个新的布雷格曼差异子类，称为指数加权分歧（EWD）。像最小DPD估计器一样，最小EWD估计器被认为是M估计量。在讨论此类估计量的渐近行为以及鲁棒性的同时，这种表征很有用。通过模拟以及现实生活中的示例比较了这两个类别的表演。我们不仅针对独立和均匀数据开发了一个估计过程，而且还针对非均质数据开发了估计过程。还考虑了基于Bregman差异的参数假设的一般检验。我们建立了我们提出的测试统计量的渐近零分布，并在应用于真实数据时探索其行为。与基于DPD的程序相比，新的EWD差异产生的推理过程似乎具有竞争力或更好。
In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new sub-class of Bregman divergences called the exponentially weighted divergence (EWD). Like the minimum DPD estimator, the minimum EWD estimator is recognised as an M-estimator. This characterisation is useful while discussing the asymptotic behaviour as well as the robustness properties of this class of estimators. Performances of the two classes are compared -- both through simulations as well as through real life examples. We develop an estimation process not only for independent and homogeneous data, but also for non-homogeneous data. General tests of parametric hypotheses based on the Bregman divergences are also considered. We establish the asymptotic null distribution of our proposed test statistic and explore its behaviour when applied to real data. The inference procedures generated by the new EWD divergence appear to be competitive or better that than the DPD based procedures.
