Geodesic
Sequential empirical process of independence
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 5, pp. 634-643.

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Uniform strong laws of large numbers and the central limit theorem for special sequential empirical process of independence for a certain class of measurable functions are considered in the paper.
Keywords: sequential empirical processes, metric entropy, Donsker theorem.
Mots-clés : Glivenko-Cantelli theorem 
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Abdurahim A. Abdushukurov; Leyla R. Kakadjanova. Sequential empirical process of independence. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 5, pp. 634-643. http://geodesic.mathdoc.fr/item/JSFU_2018_11_5_a11/

[1] A.A. Abdushukurov, L.R. Kakadjanova, “A class of special empirical processes of independence”, J. Siberian Federal Univ. Math. Phys., 8:2 (2015), 125–133 | DOI | MR

[2] J. Bae, S. Kim, “The sequential uniform law of large numbers”, Bull. Korean Math. Soc., 43:3 (2006), 479–486 | DOI | MR | Zbl

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

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

[5] Yu.V. Prokhorov, “An enlarge of S. N. Bernstein's inequality to the multivariate case”, Theory Probab. Appl., 13:3 (1968), 266–274 (in Russian) | MR