Geodesic
On Unbiased Estimation of a Vector Parameter
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 547-550

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It is shown in this paper that Rao's criterion of comparing two unbiased estimators on the basis of definiteness of the difference between their dispersion matrices is equivalent to Cramer's criterion based on their concentration ellipsoids. When the estimators have normal distributions it is shown that both the criteria have a desirable property in terms of the probabilities of the estimators lying in ellipsoids with the parameter point as the center. 
Mehra, K. L.; Ramachandramurty, P. V. On Unbiased Estimation of a Vector Parameter. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 547-550. doi: 10.4153/CMB-1972-096-3
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     author = {Mehra, K. L. and Ramachandramurty, P. V.},
     title = {On {Unbiased} {Estimation} of a {Vector} {Parameter}},
     journal = {Canadian mathematical bulletin},
     pages = {547--550},
     year = {1972},
     volume = {15},
     number = {4},
     doi = {10.4153/CMB-1972-096-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-096-3/}
}
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