Geodesic
The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables
Sbornik. Mathematics, Tome 27 (1975) no. 4, pp. 554-563 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the notion of homogeneous vector-valued $U$-statistic is introduced and a central limit theorem is proved for such statistics of a sequence of finitely dependent random variables, which generalizes analogous results for ordinary $U$-statistics. The convergence of finite-dimensional distributions of some random processes generated by $U$-statistics is also studied. Bibliography: 5 titles. 
@article{SM_1975_27_4_a6,
     author = {V. G. Mikhailov},
     title = {The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables},
     journal = {Sbornik. Mathematics},
     pages = {554--563},
     year = {1975},
     volume = {27},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_27_4_a6/}
}
TY  - JOUR
AU  - V. G. Mikhailov
TI  - The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables
JO  - Sbornik. Mathematics
PY  - 1975
SP  - 554
EP  - 563
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1975_27_4_a6/
LA  - en
ID  - SM_1975_27_4_a6
ER  - 
%0 Journal Article
%A V. G. Mikhailov
%T The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables
%J Sbornik. Mathematics
%D 1975
%P 554-563
%V 27
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1975_27_4_a6/
%G en
%F SM_1975_27_4_a6
V. G. Mikhailov. The central limit theorem for nonhomogeneous $U$-statistics of finitely dependent random variables. Sbornik. Mathematics, Tome 27 (1975) no. 4, pp. 554-563. http://geodesic.mathdoc.fr/item/SM_1975_27_4_a6/

[1] W. Hoeffding, “A class of statistics with asymptotically normal distribution”, Ann. Math. Statist., 19:3 (1948), 293–325 | DOI | MR | Zbl

[2] R. G. Miller, P. K. Sen, “Weak convergence of $U$-statistics and Von-Mises 'differentiable statistical functions”, Ann. Math. Statist., 43:1 (1972), 31–43 | DOI | MR | Zbl

[3] P. K. Sen, “Weak convergence of generalized $U$-statistics”, Ann. Prob., 2:1 (1974), 90–102 | DOI | MR | Zbl

[4] B. Abdalimov, “Asimptoticheskaya normalnost $U$-statistik dlya $s$-zavisimykh velichin”, Sluchainye protsessy i smezhnye voprosy, ch. 1, izd-vo «Fan», Tashkent, 1970, 26–30 | MR

[5] B. Abdalimov, T. L. Malevich, “O tsentralnoi predelnoi teoreme dlya $U$-statistik”, Sluchainye protsessy i statisticheskie vyvody, vyp. II, izd-vo «Fan», Tashkent, 1972, 3–9