On asymptotics of the distributions of some two-step statistical estimators of a mutlidimensional parameter

This is the authors' abstract. We don't add key points for this paper.

We study the accuracy of estimation of unknown parameters in the case of two-step statistical estimates admitting special representations. An approach to the study of such problems previously proposed by the authors is extended to the case of the estimation of a multidimensional parameter. As a result, we obtain necessary and sufficient conditions for the weak convergence of the normalized estimation error to a multidimensional normal distribution.