Geodesic
Testing a complex linear hypothesis with unknown observation weights
Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 479-483.

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A characterization theorem is proved on suitable tests for the problem of testing a complex linear hypothesis, having covariance matrices of observations in general different. 
@article{MZM_1971_10_4_a12,
     author = {I. S. Dobrokhotov},
     title = {Testing a complex linear hypothesis with unknown observation weights},
     journal = {Matemati\v{c}eskie zametki},
     pages = {479--483},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a12/}
}
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I. S. Dobrokhotov. Testing a complex linear hypothesis with unknown observation weights. Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 479-483. http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a12/