446

  • Read count445
  • Date of publication18-03-2021
  • Main LanguageRus
  • Pages20-27
Tags
Ўзбек

Bog‘liqsizlikning empirik xarakteristik protseslari uchun limit
Gauss protseslari aniqlangan. Nolinchi gipotezani tekshirish
uchun ba’zi statistikalar tavsiya etilgan.

English

For empirical characteristic process of independence limit
Gaussian process is established. For testing of zero hypothesis
some statistics are presented.

№ Name of reference
1 Abdushukurov A. A. , Kakadjanova L. R. A class of special empirical process of independence. J. Siberian Federal Univ. Math. Phys., 8(2), 2015, pp.125-133.
2 Abdushukurov A. A. , Kakadjanova L. R. Sequential empirical process of independence. J. Siberian Federal Univ. Math. Phys., 5(11), 2018, pp.634-643.
3 Abdushukurov A. A. , Kakadjanova L. R. The uniform variants of the Glivenko-Cantelli and Donsker type theorems for a sequential integral processes of independence. American J. Theor. & Appl. Stat., 9(4), 2020, pp.121-126.
4 Какаджанова Л. Р. Равномерные теоремы типа Гливенко-Кантелли и Донскера для последователь- ного интеграл процесса независимости. Бюллетень Инст. Матем., 2, 2020, с.83-91.
5 Kakadjanova L. R. Test statistics based on independence process. Bulletin of National Univer. Uzbekistan: Math & Natural Sci., 3(2), 2020, pp.178-187.
6 Cs ̈org ̋o L. R. Limit behaviour of the empirical characteristic function. Ann. Probab., 9(1), 1981, pp.130-144.
7 Dudley R. M. Uniform central limit theorems. Cambridge University Press, Cambridge, 1999.
8 Dudley R. M. Notes on empirical process. Cambridge, January 24. 2000.
9 Mason D. M. Selected defenitions and results from modern empirical process theory. Comunicaciones del CIMAT. 1-17-01, 16.03.2017 (PE).
10 Ossiander Mina. A central limit theorem under metric entropy with L2 bracketing. Ann. Probab., 3(15), 1987, pp.897-919.
11 Prokhorov Yu. An enlarge of S.N. Bernstein’s inequality to the multivariate case. Theory Probab. Appl., 3(13), 1968, pp.266-274. (In Russian)
12 Ushakov N. G. Selected topics in characteristic functions. Utrecht, The Netherlands, 1999.
13 Van der Vaart A. W. , Wellner J. A. Weak convergence and empirical processes. Springer, 1996.
14 Van der Vaart A. W. Asymptotic Statistics. Cambridge University Press, Cambridge, 1998.
15 Vapnik V. N. Statistical learning theory. Wiley, New York, 1998.
16 Yukich J. E. Weak convergence of the empirical characteristic function. Proc. American Math. Soc., 95(3), 1985, pp.470-473.
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