Geodesic
Extremal characteristics of tests for multiple hypotheses with given mutual total variation distances
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 439-463

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We consider extremal values of the characteristics of nonrandomized statistical criteria in the following case: there are $n$ hypotheses with given total variation distances. It is shown that finding the extremal values of a function of error probabilities may be reduced to solving a finite-dimensional linear programming problem. We found exact formulas for extreme values of the sum of all error probabilities in the case $n=3$.
Keywords: multiple hypothesis testing, nonrandomized tests, extremal sets of distributions.
Mots-clés : total variation distance 
@article{TVP_2016_61_3_a1,
     author = {M. P. Savelov},
     title = {Extremal characteristics of tests for multiple hypotheses with given mutual total variation distances},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {439--463},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a1/}
}
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M. P. Savelov. Extremal characteristics of tests for multiple hypotheses with given mutual total variation distances. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 439-463. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a1/