Necessary conditions for the bootstrap of the mean of a triangular array
del Barrio, E. ; Matrán, C. ; Cuesta-Albertos, J. A.
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999), p. 371-386 / Harvested from Numdam
Publié le : 1999-01-01
@article{AIHPB_1999__35_3_371_0,
     author = {del Barrio, E. and Matr\'an, C. and Cuesta-Albertos, J. A.},
     title = {Necessary conditions for the bootstrap of the mean of a triangular array},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {35},
     year = {1999},
     pages = {371-386},
     mrnumber = {1689886},
     zbl = {0930.62047},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1999__35_3_371_0}
}
del Barrio, E.; Matrán, C.; Cuesta-Albertos, J. A. Necessary conditions for the bootstrap of the mean of a triangular array. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) pp. 371-386. http://gdmltest.u-ga.fr/item/AIHPB_1999__35_3_371_0/

[1] Araujo A. and Giné E., The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York, 1980. | MR 576407 | Zbl 0457.60001

[2] Arcones M. and Giné E., The Bootstrap of the Mean with Arbitrary Bootstrap Sample Size. Ann. Inst. Henri Poincaré, Prob. Stat., Vol. 25, 1989, pp. 457-481. | Numdam | MR 1045246 | Zbl 0712.62015

[3] Athreya K.B., Bootstrap of the Mean in the Infinite Variance Case. Proceedings of the 1st World Congress of the Bernoulli Society, Y. Prohorov and V. V. Sazonov, Eds., Vol. 2, 1987, pp. 95-98. VNU Science Press, The Netherlands. | MR 1092445 | Zbl 0669.62023

[4] Breiman L., Probability, Addison-Wesley, Reading, Mass, 1968. | MR 229267 | Zbl 0174.48801

[5] Cuesta-Albertos J.A. and MATRÁN C, The asymptotic distribution of the bootstrap sample mean of an infinitésimal array. Ann. Inst. Henri Poincaré, Prob. Stat., Vol. 34, 1998, pp. 23-48. | Numdam | MR 1617729 | Zbl 0907.62018

[6] Feller W., An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York, 1966. | MR 210154 | Zbl 0138.10207

[7] Giné E. and Zinn J., Necessary conditions for the bootstrap of the mean, Ann. Statist., Vol. 17, 1989, pp. 684-691. | MR 994259 | Zbl 0672.62026

[8] Hall P., Asymptotic Properties of the Bootstrap of Heavy Tailed Distributions, Ann. Statist., Vol. 18, 1990, pp. 1342-1360. | MR 1062071 | Zbl 0714.62035

[9] Mammen E., Bootstrap, wild bootstrap, and asymptotic normality, Probab. Theory Relat. Fields, Vol. 93, 1992, pp. 439-455. | MR 1183886 | Zbl 0766.62021

[10] Swanepoel J.W.H., A Note in Proving that the (Modified) Bootstrap Works, Commun. Statist. Theory Meth., Vol. 15, 1986, pp. 3193-3203. | MR 860478 | Zbl 0623.62041