Estimations and Optimal Tests in Some Parametric Models

In the present paper, we introduce an efficient method for the estimation in the multidimensional case. The key idea is based on a good assessment of the error without using confidence intervals. The consistency of the proposed estimate is established. Consequently, we discuss the estimation in statistical tests corresponding to parametric context, and prove that this kind of estimators ensures the optimality of statistical tests. We partially extend the scope of our study to some processes. In order to examine the performance of our methodology, finite sample results are performed. This work completes and extends in nontrivial way the results obtained by Lounis (2017).