  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.
