Geodesic
Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations
Matematičeskie trudy, Tome 11 (2008) no. 2, pp. 3-19 
I. S. Borisov; N. V. Volodko. Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations. Matematičeskie trudy, Tome 11 (2008) no. 2, pp. 3-19. http://geodesic.mathdoc.fr/item/MT_2008_11_2_a0/
@article{MT_2008_11_2_a0,
     author = {I. S. Borisov and N. V. Volodko},
     title = {Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--19},
     year = {2008},
     volume = {11},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2008_11_2_a0/}
}
TY  - JOUR
AU  - I. S. Borisov
AU  - N. V. Volodko
TI  - Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations
JO  - Matematičeskie trudy
PY  - 2008
SP  - 3
EP  - 19
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MT_2008_11_2_a0/
LA  - ru
ID  - MT_2008_11_2_a0
ER  - 
%0 Journal Article
%A I. S. Borisov
%A N. V. Volodko
%T Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations
%J Matematičeskie trudy
%D 2008
%P 3-19
%V 11
%N 2
%U http://geodesic.mathdoc.fr/item/MT_2008_11_2_a0/
%G ru
%F MT_2008_11_2_a0

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

Exponential inequalities are obtained for the distribution tails of canonical (degenerate) $U$- and $V$-statistics of an arbitrary order based on samples from a stationary sequence of observations satisfying $\varphi$-mixing.

[1] Borisov I. S., “Approksimatsiya raspredelenii statistik Mizesa s mnogomernymi yadrami”, Sib. mat. zhurn., 32:4 (1991), 20–35 | MR | Zbl

[2] Borisov I. S., Bystrov A. A., “Predelnye teoremy dlya kanonicheskikh statistik Mizesa, postroennykh po zavisimym nablyudeniyam”, Sib. mat. zhurn., 47:6 (2006), 1205–1217 | MR | Zbl

[3] Borisov I. S., Volodko N. V., “Ortogonalnye ryady i predelnye teoremy dlya kanonicheskikh $U$- i $V$-statistik ot statsionarno svyazannykh nablyudenii”, Mat. trudy, 11:1 (2008), 25–48 | MR

[4] Korolyuk V. S., Borovskikh Yu. V., Teoriya $U$-statistik, Naukova Dumka, Kiev, 1989 | MR | Zbl

[5] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR

[6] Adamczak R., “Moment inequalities for $U$-statistics”, Ann. Probab., 34:6 (2006), 2288–2314 | DOI | MR | Zbl

[7] Arcones M. A., Giné E., “Limit theorems for $U$-processes”, Ann. Probab., 21:3 (1993), 1494–1542 | DOI | MR | Zbl

[8] Dedecker J., Prieur C., “New dependence coefficients. Examples and applications to statistics”, Probab. Theory Related Fields, 132:2 (2005), 203–236 | DOI | MR | Zbl

[9] Giné E., Latała R., Zinn J., “Exponential and moment inequalities for $U$-statistics”, High Dimensional Probability, II (Seattle, WA, 1999), Progr. Probab., 47, Birkhäuser, Boston, 2000, 13–38 | MR | Zbl

[10] Hoeffding W., “Probability inequalities for sums of bounded random variables”, J. Amer. Statist. Assoc., 58 (1963), 13–30 | DOI | MR | Zbl