Geodesic
Asymptotically optimal criteria for testing parametric hypothesis on the distribution of a random vector. I
Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 89-116 
A. V. Ivanov. Asymptotically optimal criteria for testing parametric hypothesis on the distribution of a random vector. I. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 89-116. http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a5/
@article{MVK_2015_6_3_a5,
     author = {A. V. Ivanov},
     title = {Asymptotically optimal criteria for testing parametric hypothesis on the distribution of a~random {vector.~I}},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {89--116},
     year = {2015},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a5/}
}
TY  - JOUR
AU  - A. V. Ivanov
TI  - Asymptotically optimal criteria for testing parametric hypothesis on the distribution of a random vector. I
JO  - Matematičeskie voprosy kriptografii
PY  - 2015
SP  - 89
EP  - 116
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a5/
LA  - ru
ID  - MVK_2015_6_3_a5
ER  - 
%0 Journal Article
%A A. V. Ivanov
%T Asymptotically optimal criteria for testing parametric hypothesis on the distribution of a random vector. I
%J Matematičeskie voprosy kriptografii
%D 2015
%P 89-116
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a5/
%G ru
%F MVK_2015_6_3_a5

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

We construct asymptotically optimal criteria for testing two simple hypotheses on the scalar parameter of discrete noise in a combined semicontinuos communication channel for the triangular scheme. Probabilistic characteristics of these criteria are obtained (in particular, asymptotics of the minimal sample size for given error probabilities of two kinds). It is shown that the minimal sample size depends essentially on the channel parameters.

[1] Arbekov I. M., “Optimalnaya diskretizatsiya nablyudenii slabykh signalov pri ogranichenii na skorost kvantovaniya”, Problemy peredachi informatsii, 34:1 (1998), 69–76 | MR | Zbl

[2] Borovkov A. A., Matematicheskaya statistika, 4-e izd., Lan, Sankt-Peterburg–Moskva–Krasnodar, 2010, 704 pp.

[3] Verner M., Osnovy kodirovaniya, Tekhnosfera, M., 2004, 288 pp.

[4] Gaek Ya., Shidak Z., Teoriya rangovykh kriteriev, Nauka, M., 1971, 376 pp.

[5] Gnedenko B. V., Kurs teorii veroyatnostei, 6-e izd., Nauka, M., 1988, 448 pp. | MR

[6] Ivanov A. V., “Asimptoticheski naibolee moschnyi kriterii razlicheniya gipotez o raspredelenii sluchainogo vektora”, 10-ya Obscheros. nauch. konf. MaBIT-2011, Materialy sektsii “Matematicheskie problemy informatsionnoi bezopasnosti”, MAKS-PRESS, M., 2012, 93–97

[7] Ivanov A. V., “Asimptoticheski optimalnye kriterii v zadache razlicheniya gipotezo raspredelenii sluchainogo vektora”, Obozr. prikl. i promyshl. matem., 20:2 (2013), 139–141

[8] Ivanov A. V., “Asimptoticheski optimalnye kriterii v zadache razlicheniya gipotez o raspredelenii sluchainogo vektora. II”, Obozr. prikl. i promyshl. matem., 20:4 (2013), 548–550

[9] Ivanov A. V., “Asimptoticheski optimalnye kriterii v zadache razlicheniya gipotez o raspredelenii sluchainogo vektora. III”, Obozr. prikl. i promyshl. matem., 21:1 (2014), 58–60

[10] Maksimov Yu. I., “Postroenie i analiz statisticheskikh kriteriev dlya nekotorykh skhem sluchainykh posledovatelnostei so znacheniyami iz polya $GF(q)$”, Trudy po diskretnoi matematike, 5, 2002, 159–166

[11] Pazizin S. V., “Obnaruzhenie i priem posledovatelnosti signalov, iskazhennykh sluchainoi pomekhoi i nezavisimym shumom”, Problemy peredachi informatsii, 34:1 (1998), 46–55 | MR | Zbl

[12] Pazizin S. V., “Veroyatnosti pravilnogo dekodirovaniya dlya kanala s additivnym normalnym shumom i dvoichnogo simmetrichnogo kanala pri sluchainom vybore kodovykh slov”, Diskretnaya matematika, 12:2 (2000), 93–98 | DOI | MR | Zbl

[13] Petrov V. V., Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987, 320 pp. | MR

[14] Rusas Dzh., Kontigualnost veroyatnostnykh mer, Mir, M., 1975, 256 pp. | MR

[15] Chibisov D. M., “Teorema o dopustimykh kriteriyakh i ee primenenie k odnoi asimptoticheskoi zadache proverki gipotez”, Teoriya veroyatn. i ee primen., 21:1 (1967), 96–111 | MR | Zbl

[16] Arbekov I. M., “Asymptotically optimum detection of a weak signal sequence with random time delays”, IEEE Trans. Inf. Theory, 41:4 (1995), 1169–1174 | DOI | Zbl

[17] Kassam S. A., Signal detection in non-gaussian noise, Springer-Verlag, New-York, 1988, 235 pp. | MR

[18] Miller J. H., Thomas J. B., “Detectors for discrete-time signals in non-gaussian noise”, IEEE Trans. Inf. Theory, 18:2 (1972), 241–250 | DOI | MR | Zbl