Zhang (2019) presented a general estimation approach based on the Gaussian distribution for general parametric models where the likelihood of the data is difficult to obtain or unknown, but the mean and variance-covariance matrix are known. Castilla and Zografos (2021) extended the method to density power divergence-based estimators, which are more robust than the likelihood-based Gaussian estimator against data contamination. In this paper we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. Also, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, in special in testing composite null hypothesis, and provide here constrained estimators to inherent restrictions of the underlying distribution. Further, we derive robust Rao-type test statistics based on the MDPDGE for testing simple null hypothesis and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.
翻译:Zhang (2019年) 提出了一个基于Gausian分布法的总体估计方法,根据Gausian分布法,一般参数模型的密度差很难获得或未知,但数据的平均和差异差异性矩阵是已知的。Castilla 和 Zografos (2021年) 将这种方法扩大到密度功率差测算器,这些测算器比基于可能性的Gaussian 估测器更能防止数据污染。在本文中,我们引入了限制最小密度差高西亚估计仪(MDPDGE),并研究其主要的无症状特性。此外,我们通过其影响功能分析来研究它是否稳健。在许多实际情况下,特别在综合无效假设测试中,需要有限制性的估测器,并在此对基本分布的内在限制提供有限的估测器。此外,我们根据MDPDDGGE测试简单无效假设得出强的Rao型测试统计数据,我们通过模拟研究从经验上评估方法的效率和稳健性。