Geodesic
Statistical methods of search for coordinate set on which a~random vector has bans
Prikladnaâ diskretnaâ matematika, no. 2 (2015), pp. 5-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

A stationary sequence of random vectors of length $L$ with the distribution of a random vector $\xi$ is observed. Coordinates of vectors in it take values in a finite set. The following hypothesis is considered: there is a set $\Theta\subset\{1,\dots,L\}$ such that the subvector $\xi_\Theta$ (being the projection of $\xi$ onto coordinates with numbers in $\Theta$) has the distribution of a given random vector $\eta$ with the distribution having bans. A concordance criterion is constructed by the analysis of an empirical distribution bans. In the case of the hypothesis validity (a priori), three algorithms to search for a part of $\Theta$ are proposed. They work under various portions of the information about the random vector $\eta$ distribution.
Keywords: statistical test
Mots-clés : bans of distributions. 
@article{PDM_2015_2_a0,
     author = {O. V. Denisov},
     title = {Statistical methods of search for coordinate set on which a~random vector has bans},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--20},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_2_a0/}
}
TY  - JOUR
AU  - O. V. Denisov
TI  - Statistical methods of search for coordinate set on which a~random vector has bans
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2015
SP  - 5
EP  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2015_2_a0/
LA  - ru
ID  - PDM_2015_2_a0
ER  - 
%0 Journal Article
%A O. V. Denisov
%T Statistical methods of search for coordinate set on which a~random vector has bans
%J Prikladnaâ diskretnaâ matematika
%D 2015
%P 5-20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2015_2_a0/
%G ru
%F PDM_2015_2_a0
O. V. Denisov. Statistical methods of search for coordinate set on which a~random vector has bans. Prikladnaâ diskretnaâ matematika, no. 2 (2015), pp. 5-20. http://geodesic.mathdoc.fr/item/PDM_2015_2_a0/

[1] Grusho A. A., Timonina E. E., “Prohibitions in discrete probabilistic statistical problems”, Diskretnaya Matematika, 23:2 (2011), 53–58 (in Russian) | DOI | MR | Zbl

[2] Grusho A. A., Grusho N. A., Timonina E. E., “Statistical techniques of bans determination of probability measures in discrete spaces”, Inform. Primen., 7:1 (2013), 54–57 (in Russian)

[3] Mikhaylov V. G., Chistyakov V. P., “Problems of the finite automata theory associated with a number of inverse images of the output sequence”, Obozrenie Prikl. i Promyshl. Matem. Ser. Diskretn. Matem., 1:1 (1994), 7–32 (in Russian) | MR | Zbl

[4] Sumarokov S. N., “Prohibitions of binary functions and reversibility for a class of encoders”, Obozrenie Prikl. i Promyshl. Matem. Ser. Diskretn. Matem., 1:1 (1994), 33–55 (in Russian) | MR | Zbl

[5] Grusho A. A., Timonina E. E., “Some relations between discrete statistical problems and properties of probability measures on topological spaces”, Diskretnaya Matematika, 18:4 (2006), 128–136 (in Russian) | DOI | MR | Zbl