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. Here, we present the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study it asymptotic and robustness properties through it asymptotic distribution and influence function, respectively. Restricted estimators are required in many practical situations 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 composite null hypothesis and we deduce explicit expression for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the methodthrough 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,但数据的平均分布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动力差异估计器,这些测算器比基于可能性的Gaussian 估计器更能防止数据污染。在这里,我们提出了限制最小密度差Gaussian 估计器(MDPDGE), 并分别通过该测算器的无症状和稳健性特性, 研究该测算器的分布和影响功能。在许多实际情况下,需要有限制性的测算器, 并在此对基本分布的内在限制提供有限的估计器。 此外,我们根据MDDDDGGE测试了强型测算器测试综合无效假设并推断出一些重要分布的清晰表达法。最后,我们通过模拟研究对方法的效率和稳健性进行了实验性评价。