Geodesic
The minimal essentially complete class of discrimination rules in the case of unknown higher moments of the distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 832-834

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A multivariate problem of testing a complex hypothesis against a complex alternative determined both by the known values of mean vectors and covariance matrices is considered. As the loss function the maximal probability of incorrect classification is chosen. It is shown that, unlike the case of commonly used additional assumptions of normality, the minimal essentially complete class of decision rules consists of linear type rules. 
@article{TVP_1974_19_4_a12,
     author = {Yu. N. Zhezhel'},
     title = {The minimal essentially complete class of discrimination rules in the case of unknown higher moments of the distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {832--834},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a12/}
}
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Yu. N. Zhezhel'. The minimal essentially complete class of discrimination rules in the case of unknown higher moments of the distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 832-834. http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a12/