@article{AIHPB_1998__34_4_425_0, author = {Castelle, Nathalie and Laurent-Bonvalot, Fran\c{c}oise}, title = {Strong approximations of bivariate uniform empirical processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {425--480}, publisher = {Gauthier-Villars}, volume = {34}, number = {4}, year = {1998}, mrnumber = {1632841}, zbl = {0915.60048}, language = {en}, url = {http://www.numdam.org/item/AIHPB_1998__34_4_425_0/} }
TY - JOUR AU - Castelle, Nathalie AU - Laurent-Bonvalot, Françoise TI - Strong approximations of bivariate uniform empirical processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1998 SP - 425 EP - 480 VL - 34 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPB_1998__34_4_425_0/ LA - en ID - AIHPB_1998__34_4_425_0 ER -
%0 Journal Article %A Castelle, Nathalie %A Laurent-Bonvalot, Françoise %T Strong approximations of bivariate uniform empirical processes %J Annales de l'I.H.P. Probabilités et statistiques %D 1998 %P 425-480 %V 34 %N 4 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPB_1998__34_4_425_0/ %G en %F AIHPB_1998__34_4_425_0
Castelle, Nathalie; Laurent-Bonvalot, Françoise. Strong approximations of bivariate uniform empirical processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) no. 4, pp. 425-480. http://www.numdam.org/item/AIHPB_1998__34_4_425_0/
[1] Tail of behaviour for suprema of empirical process. Annals of probability, Vol 14, 1986, pp. 1-30. | MR | Zbl
and ,[2] Probability inequalities for the sum of independants random variables. J. AM. Statis. Assoc., Vol. 57, 1962, pp. 33-45. | Zbl
,[3] Hungarian constructions from the non asymptotic view point. Annals of Probability, Vol 17, 1989, pp. 239-256. | MR | Zbl
and ,[4] The asymptotic representation of the sample distribution function. Bull. Amer. Math. Soc., Vol 75, 1969, pp. 545-547. | MR | Zbl
,[5] Strong approximations in probability and statistics. Academic Press, 1981, New York. | MR | Zbl
and ,[6] Investigations concerning the empirical distribution function. English translation in Selected Trans. Math. Statis. Probab., Vol 15, 1981, pp. 229-317. | Zbl
,[7] Weighted Approximations in Probability and Statistics. Wiley & Sons, 1993. | Zbl
and ,[8] Stochastic process, Wiley, 1953, New York. | MR | Zbl
,[9] Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann. Math. Stat., Vol. 33, 1956, pp. 642-669. | MR | Zbl
, and ,[10] On the deviations in the Skorohod-Strassen approximation scheme. Z. Wahrschein. Verw. Geb., Vol. 13, 1969, pp. 321-332. | MR | Zbl
,[11] Skorohod embedding of multivariate R. V.'s, and the sample D.F.Z. Z. Wahrschein. Verw. Geb., Vol. 24, 1972, pp. 1-35. | MR | Zbl
,[12] An approximation of partial sums of independent RV'- and the sample D. F. I. Z. Warschein. Verw. Geb., Vol. 32, 1975, pp. 111-131. | MR | Zbl
, and ,[13] A strong invariance theorem for the tail empirical process. Annales de l'I.H.P., Vol. 24, 1988. | Numdam | MR | Zbl
,[14] A refinement of the KMT inequality for the uniform empirical process. Annals of Probability, Vol. 15, 1987, pp. 871-884. | MR | Zbl
and Van ,[15] The tight constant of the Dvorestsky-Kiefer-Wolfowitz inequality. Annals of Probability, Vol. 18, 1990, pp.1269-1283. | MR | Zbl
,[16] Empirical processes with applications to statistics. Wiley & Sons, 1986.
and ,[17] On a representation of random variables. Th. Proba. Appl., Vol. 21, 1976, pp. 628-632. | MR | Zbl
,[18] Sharper bounds for empirical process. Annals of Probability, Vol. 22, 1994, pp. 28-76. | MR | Zbl
,[19] A remark on the approximation of the sample D.F. in the multidimensional case. Periodica Math. Hung., Vol. 8, 1977, pp. 53-55. | MR | Zbl
,[20] Limit theorems for the ratio of the empirical distribution function to the true distribution function. Z. Warschein. Verw. Geb., Vol. 45, 1978, pp. 73-88. | MR | Zbl
,