A class of special empirical processes of independence
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 125-133.

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

In this paper we investigate the asymptotic properties of one class of empirical processes for certain classes of integrable functions.
Keywords: empirical processes, metric entropy, Donsker’s theorem.
Mots-clés : Glivenko–Cantelli theorem
@article{JSFU_2015_8_2_a0,
     author = {Abdurahim A. Abdushukurov and Leyla R. Kakadjanova},
     title = {A class of special empirical processes of independence},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {125--133},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a0/}
}
TY  - JOUR
AU  - Abdurahim A. Abdushukurov
AU  - Leyla R. Kakadjanova
TI  - A class of special empirical processes of independence
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2015
SP  - 125
EP  - 133
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a0/
LA  - en
ID  - JSFU_2015_8_2_a0
ER  - 
%0 Journal Article
%A Abdurahim A. Abdushukurov
%A Leyla R. Kakadjanova
%T A class of special empirical processes of independence
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2015
%P 125-133
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a0/
%G en
%F JSFU_2015_8_2_a0
Abdurahim A. Abdushukurov; Leyla R. Kakadjanova. A class of special empirical processes of independence. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 125-133. http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a0/

[1] K. S. Alexander, “Probability inequalities for empirical processes and a law of the iterated logarithm”, Ann. Probab., 12:4 (1984), 1041–1067 | DOI | MR | Zbl

[2] R. M. Dudley, “Central limit theorems for empirical measures”, Ann. Probab., 6 (1978), 899–929 | DOI | MR | Zbl

[3] P. Gaensler, W. Stute, “Empirical processes: a survey of results for independent and identically distributed random variables”, Ann. Probab., 7:2 (1979), 193–243 | DOI | MR

[4] E. Gine, J. Zinn, “Some limit theorems for empirical processes”, Ann. Probab., 12:4 (1984), 929–989 | DOI | MR | Zbl

[5] G. R. Shorack, J. A. Wellner, Empirical processes with applications to statistics, John Wiley Sons, 1986 | MR

[6] A. W. Van der Vaart, J. A. Wellner, Weak convergence and empirical processes, Springer, 1996 | MR | Zbl

[7] A. W. Van der Vaart, Asymptotic Statistics, Cambridge University Press, 1998 | MR | Zbl

[8] A. A. Abdushukurov, L. R. Kakadjanova, “About one class of empirical processes”, Proceedings of the XVI International Conference on eventological mathematics and related issues (Krasnoyarsk, 2012), 31 (in Russian) | Zbl

[9] A. A. Abdushukurov, L. R. Kakadjanova, “Asymptotical Gaussian distribution of a class of empirical processes”, Problems of modern topology and its applications, Proc. of reports International Conf. (Tashkent, 2013), 100–102 (in Russian)

[10] A. A. Abdushukurov, L. R. Kakadjanova, “An empirical processes of independence by class of measured functions”, Statistics and its Applications, Materials of conf. (Tashkent, 2013), 24–29 (in Russian)

[11] A. A. Abdushukurov, L. R. Kakadjanova, “An empirical processes of independence indexed by class of measured functions”, Acta National University of Uzbekistan, 1:2 (2014), 15–20 (in Russian)

[12] A. A. Abdushukurov, On some estimates of the distribution function under random censorship, Conference of young Scientists, Math. Inst. Acad. Sci. Uzbek SSR, No 8756, VINITI, 1984 (in Russian)

[13] A. A. Abdushukurov, Nonparametric estimation in proportional hazards model, No 3448-87, VINITI, 1987 (in Russian)

[14] A. A. Abdushukurov, “Estimating of the probability density and intensity function of the Koziol–Green model of random censoring”, Sankhya: The Indian J. Statist., 48 (1987), 150–168 | MR

[15] S. Csörgő, “Estimation in the proportional hazards model of random censorship”, Statistics, 19:3 (1988), 437–463 | DOI | MR

[16] S. Csörgő, J. J. Faraway, “The paradoxical nature of the proportional hazards model of random censorship”, Statistics, 31 (1998), 67–78 | DOI | MR | Zbl