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)提出了一种基于高斯分布的通用参数模型估计方法，适用于数据似然函数难以获取或未知但其均值与方差-协方差矩阵已知的情形。Castilla与Zografos (2021)将该方法扩展至基于密度功率散度的估计器，此类估计器相较于基于似然的高斯估计对数据污染具有更强稳健性。本文引入受限最小密度功率散度高斯估计器(MDPDGE)并研究其渐近性质，同时通过影响函数分析考察其稳健性。受限估计器在诸多实际场景中具有重要应用，尤其在复合零假设检验中，可为潜在分布的内在约束提供受限估计。进一步，我们基于MDPDGE推导出适用于简单零假设检验的稳健Rao型检验统计量，并给出若干关键分布的显式表达式。最后，通过仿真研究实证评估该方法的效率与稳健性。