| Abstract: | The extensive use of maximum likelihood estimates underscores the importance of the problem of statistical estimation of their
errors. These estimates are of utmost importance in cases where the family of normal distributions and the families related
to the normal distributions are considered 1, 2, 4]. The mean square errors of the maximum likelihood estimates of the normal density were investigated in the author's paper
3]. The mean square errors of statistical estimates of some families of densities related to the normal distributions were
considered in the papers 4–6]. In the present paper, we obtain an asymptotic expansion of the mean square error of the maximum likelihood estimates of
the densities of the joint distribution of sufficient statistics of the family of multivariate normal distributions. The results
obtained allow us to construct the mean square errors of the maximum likelihood estimates for the chi-square density and Wishart's
density.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 4–11, Perm. 1990. |
