Felipe Ortega, ÁngelJaenada Malagón, MaríaMiranda Menéndez, PedroPardo Llorente, Leandro2023-06-222023-06-222023-03-172227-739010.3390/math11061480https://hdl.handle.net/20.500.14352/72964In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a 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 studyengAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttps://doi.org/10.3390/math11061480https://www.mdpi.com/2227-7390/11/6/1480open access519.22Gaussian estimatorMinimum density power divergence Gaussian estimatorRobustnessInfluence functionRao-type testsElliptical family of distributionsEstadística matemática (Matemáticas)1209 Estadística