Necessary conditions for the bootstrap of the mean of a triangular array

E. del Barrio; C. Matrán; J. A. Cuesta-Albertos

Annales de l'I.H.P. Probabilités et statistiques (1999)

  • Volume: 35, Issue: 3, page 371-386
  • ISSN: 0246-0203

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del Barrio, E., Matrán, C., and 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 35.3 (1999): 371-386. <http://eudml.org/doc/77633>.

@article{delBarrio1999,
author = {del Barrio, E., Matrán, C., Cuesta-Albertos, J. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {central limit theorem; U-statistics; bootstrap mean; arbitrary resampling sizes; necessary conditions; triangular arrays},
language = {eng},
number = {3},
pages = {371-386},
publisher = {Gauthier-Villars},
title = {Necessary conditions for the bootstrap of the mean of a triangular array},
url = {http://eudml.org/doc/77633},
volume = {35},
year = {1999},
}

TY - JOUR
AU - del Barrio, E.
AU - Matrán, C.
AU - Cuesta-Albertos, J. A.
TI - Necessary conditions for the bootstrap of the mean of a triangular array
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1999
PB - Gauthier-Villars
VL - 35
IS - 3
SP - 371
EP - 386
LA - eng
KW - central limit theorem; U-statistics; bootstrap mean; arbitrary resampling sizes; necessary conditions; triangular arrays
UR - http://eudml.org/doc/77633
ER -

References

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  1. [1] Araujo A. and Giné E., The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York, 1980. Zbl0457.60001MR576407
  2. [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. Zbl0712.62015MR1045246
  3. [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. Zbl0669.62023MR1092445
  4. [4] Breiman L., Probability, Addison-Wesley, Reading, Mass, 1968. Zbl0174.48801MR229267
  5. [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. Zbl0907.62018MR1617729
  6. [6] Feller W., An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York, 1966. Zbl0138.10207MR210154
  7. [7] Giné E. and Zinn J., Necessary conditions for the bootstrap of the mean, Ann. Statist., Vol. 17, 1989, pp. 684-691. Zbl0672.62026MR994259
  8. [8] Hall P., Asymptotic Properties of the Bootstrap of Heavy Tailed Distributions, Ann. Statist., Vol. 18, 1990, pp. 1342-1360. Zbl0714.62035MR1062071
  9. [9] Mammen E., Bootstrap, wild bootstrap, and asymptotic normality, Probab. Theory Relat. Fields, Vol. 93, 1992, pp. 439-455. Zbl0766.62021MR1183886
  10. [10] Swanepoel J.W.H., A Note in Proving that the (Modified) Bootstrap Works, Commun. Statist. Theory Meth., Vol. 15, 1986, pp. 3193-3203. Zbl0623.62041MR860478

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