Geodesic
On detection of Gaussian stochactic vectors
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 250-257

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The problem of minimax detection of a Gaussian random signal vector in white Gaussian additive noise has been considered. We suppose that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belongs to the given set ${\mathcal E}$. We have investigated when it is possible to replace the set ${\mathcal E}$ (and, in particular, by a single point $\boldsymbol{\sigma}_{0}$) by a smaller set ${\mathcal E}_{0}$ without quality loss.
Keywords: detection, minimax, reduction. 
@article{UZKU_2018_160_2_a4,
     author = {M. V. Burnashev},
     title = {On detection of {Gaussian} stochactic vectors},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {250--257},
     publisher = {mathdoc},
     volume = {160},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2018_160_2_a4/}
}
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M. V. Burnashev. On detection of Gaussian stochactic vectors. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 160 (2018) no. 2, pp. 250-257. http://geodesic.mathdoc.fr/item/UZKU_2018_160_2_a4/