References
Yu. V. Borovskikh, Theory ofU-statistics in Hilbert space [in Russian], Preprint 86.78, Inst. of Mathematics, Kiev 1986, p. 56.
V. S. Korolyuk and Yu. V. Borovskikh, Rate of convergence in the central limit theorem forUH-statistics,Ukrain Mat. Zh.,42 (8), 1043–1050 (1990).
T. L. Malevich and B. Abdalimov, Probabilities of large deviations forU-statistics,Theory Probab. Appl.,24 (1), 215–220 (1979).
M. Vandemaele, On probabilities of large deviations forU-statistics,Theory Probab. Appl.,27 (3), 573–574 (1982).
A. K. Aleškevičienė, Probabilities of large deviations forU-statistics and for Mises functionals,Theory Probab. Appl. 35 (1), 3–14 (1990).
A. K. Aleškevičienė, Large deviations forU-statistics,Liet. Mat. Rinkinys,32 (1), 7–19 (1992).
Yu. V. Borovskikh,U-statistics in Banach spaces,Acta Appl. Math.,35 (3), 285–298 (1994).
A. I. Račkauskas, Probabilities of large deviations in the Linnik zones in Hilbert spaces,Liet. Mat. Rinkinys,28 (3), 520–533 (1988).
W. Hoeffding, A class of statistics with asymptotically normal distribution,Ann. Math. Statist.,19, 293–325 (1948).
R. Bentkus and R. Rudzkis, On exponential estimates of the distribution of random variables,Liet. Mat. Rinkinys,20 (1), 15–30 (1980).
B. A. Zalesskii, Probabilities of large deviations in Hilbert space,Theory Probab. Appl.,34 (4), 650–655 (1989).
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Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 141–151, April–June, 1995.
Translated by A. Aleškevičiene
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Aleškevičienė, A., Borovskikh, J. On probabilities of large deviations for UH-statistics. Lith Math J 35, 112–120 (1995). https://doi.org/10.1007/BF02335535
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DOI: https://doi.org/10.1007/BF02335535