Ivanov, A. V. Asymptotically optimal criteria for testing hypotheses on the distribution of a random vector. II. (Russian. English summary) Zbl 1476.62049 Mat. Vopr. Kriptografii 6, No. 4, 49-64 (2015). Summary: Asymptotically optimum criteria for testing two simple hypotheses on the vector parameters of the distribution of discrete noise in the combined semicontinuous communication channel are constructed. A probabilistic characteristics of these criteria (in particular, asymptotically minimal sample size guaranteeing the given values of error probabilities of two kinds) are obtained. It is shown that the minimal sample size depends on the relations between the channel patameters.For Part I, see [the author, ibid. 6, No. 3, 89–116 (2015; Zbl 1476.62048)]. Cited in 1 Review MSC: 62F03 Parametric hypothesis testing 94A05 Communication theory Keywords:asymptotically optimal criterion; combined semicontinuous communication channel; asymptotically minimal sample size Citations:Zbl 1476.62048 × Cite Format Result Cite Review PDF Full Text: DOI MNR References: [1] Arbekov I. M., “Optimalnaya diskretizatsiya nablyudenii slabykh signalov pri ogranichenii na skorost kvantovaniya”, Problemy peredachi informatsii, 34:1 (1998), 69-76 · Zbl 0932.94015 [2] Borovkov A. A., Matematicheskaya statistika, 4-e izd., Lan, Sankt-Peterburg-Moskva-Krasnodar, 2010, 704 pp. [3] Verner M., Osnovy kodirovaniya, Ser. “Mir programmirovaniya”, 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. · Zbl 0645.60001 [6] Ivanov A. V., “Asimptoticheski naibolee moschnyi kriterii razlicheniya gipotez o raspredelenii sluchainogo vektora”, Desyataya obscheross. nauchn. konf. “Matematika i bezopasnost informatsionnykh tekhnologii”, MaBIT-2011 (MGU, 13 oktyabrya 2011 g.), Materialy sektsii “Matematicheskie problemy informatsionnoi bezopasnosti”, MAKS-PRESS, M., 2012, 93-97 [7] Ivanov A. V., “Asimptoticheski optimalnye kriterii v zadache razlicheniya gipotez o raspredelenii sluchainogo vektora”, Obozr. prikl. 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. 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. promyshl. matem., 21:1 (2014), 58-60 [10] Ivanov A. V., “Asimptoticheski optimalnye kriterii v zadache razlicheniya parametricheskikh gipotez o raspredelenii sluchainogo vektora. I”, Matematicheskie voprosy kriptografii, 6:3 (2015), 89-116 · Zbl 1476.62048 [11] Korn G., Korn T., Spravochnik po matematike, Nauka, M., 1968, 720 pp. [12] Pazizin S. V., “Obnaruzhenie i priem posledovatelnosti signalov, iskazhennykh sluchainoi pomekhoi i nezavisimym shumom”, Problemy peredachi informatsii, 34:1 (1998), 46-55 · Zbl 1031.94505 [13] 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 · Zbl 1011.94009 · doi:10.4213/dm333 [14] Petrov V. V., Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987, 320 pp. · Zbl 0621.60022 [15] Rusas Dzh., Kontigualnost veroyatnostnykh mer, Mir, M., 1975, 256 pp. [16] Chibisov D. M., “Teorema o dopustimykh kriteriyakh i ee primenenie k odnoi asimptoticheskoi zadache proverki gipotez”, Teoriya veroyatnostei i ee primeneniya, 12:1 (1967), 96-111 · Zbl 0214.45802 [17] Arbekov I. M., “Asymptotically optimum detection of a weak signal sequence with random time delays”, IEEE Trans. Inf. Theory, 41:4 (1995), 1169-1174 · Zbl 0830.94003 · doi:10.1109/18.391264 [18] Kassam Saleem A., Signal detection in non-Gaussian noise, Springer-Verlag, New York, 1988, 235 pp. [19] Miller James H., Thomas John B., “Detectors for discrete-time signals in non-Gaussian noise”, IEEE Transactions on Information Theory, 18:2 (1972), 241-250 · Zbl 0231.94028 · doi:10.1109/TIT.1972.1054787 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.