The bootstrap of the mean with arbitrary bootstrap sample size

Miguel A. Arcones; Evarist Giné

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 4, page 457-481
  • ISSN: 0246-0203

How to cite

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Arcones, Miguel A., and Giné, Evarist. "The bootstrap of the mean with arbitrary bootstrap sample size." Annales de l'I.H.P. Probabilités et statistiques 25.4 (1989): 457-481. <http://eudml.org/doc/77360>.

@article{Arcones1989,
author = {Arcones, Miguel A., Giné, Evarist},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {bootstrap of the mean; a.s. bootstrap; bootstrap in probability; bootstrap central limit theorem; conditional distribution; weak convergence; domain of attraction of the normal law; domain of attraction of a stable law},
language = {eng},
number = {4},
pages = {457-481},
publisher = {Gauthier-Villars},
title = {The bootstrap of the mean with arbitrary bootstrap sample size},
url = {http://eudml.org/doc/77360},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Arcones, Miguel A.
AU - Giné, Evarist
TI - The bootstrap of the mean with arbitrary bootstrap sample size
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 4
SP - 457
EP - 481
LA - eng
KW - bootstrap of the mean; a.s. bootstrap; bootstrap in probability; bootstrap central limit theorem; conditional distribution; weak convergence; domain of attraction of the normal law; domain of attraction of a stable law
UR - http://eudml.org/doc/77360
ER -

References

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  1. [1] A. De Acosta and E. Giné, Convergence of Moments and Related Functionals in the Central Limit Theorem in Banach Spaces, Zeits. Wahrs. Verw. Geb., Vol. 48, 1979, pp. 213-231. Zbl0388.60008MR534846
  2. [2] A. Araujo and E. Giné, The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York, 1980. Zbl0457.60001MR576407
  3. [3] K.B. Athreya, Bootstrap for the Mean in the Infinite Variance Case, Technical report 86-22, Dept. of Statistics, Iowa State University, 1984. 
  4. [4] K.B. Athreya, Bootstrap for the Mean in the Infinite Variance Case, II, Technical Report 86-21, Dept. of Statistics, Iowa State University, 1985. 
  5. [5] D.J. Bickel and D.A. Freedman, Some Asymptotic Theory for the Bootstrap, Ann. Statist., Vol. 9, 1981, pp. 1196-1217. Zbl0449.62034MR630103
  6. [6] S. Csörgö and D. Mason, Bootstrapping Empirical Functions, Ann. Statist., Vol. 17, n° 4, 1989. Zbl0701.62057MR1026292
  7. [7] B. Efron, Bootstrap Methods: Another Look at the Jacknife, Ann. Statist., Vol. 7, 1979, pp. 1-26. Zbl0406.62024MR515681
  8. [8] W. Feller, An Introduction to Probability Theory and its Applications, II, Wiley, New York, 1971. Zbl0219.60003MR270403
  9. [9] E. Giné, Sums of Independent Random Variables and Sum of Their Squares, Publicacions Seccio Mat. U.A.B., Vol. 22, 1976, pp. 127-132. MR768397
  10. [10] E. Giné and J. Zinn, Some Limit Theorems for Empirical Processes, Ann. Probability, Vol. 12, 1984, pp. 929-989. Zbl0553.60037MR757767
  11. [11] E. Giné and J. Zinn, Bootstrapping General Empirical Measures, Ann. Probability, 1989 (to appear). Zbl0706.62017MR1055437
  12. [12] E. Giné and J. Zinn, Necessary Conditions for the Boostrap of the Mean, Ann. Statist., Vol. 17, 1989, pp. 684-691. Zbl0672.62026MR994259
  13. [13] J. Hoffmann-Jorgensen, Sums of Independent Banach Space Valued Random Variables, Studia Math., Vol. 52, 1974, pp. 159-186. Zbl0265.60005MR356155
  14. [14] M. Loève, Probability Theory, 3rd Edition, VanNostrand-Reinhold, Princeton, New Jersey, 1963. Zbl0108.14202
  15. [15] W. Stout, Almost Sure Convergence, Academic Press, New York, 1974. Zbl0321.60022MR455094

Citations in EuDML Documents

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  1. Miguel A. Arcones, Evarist Giné, Additions and correction to “The bootstrap of the mean with arbitrary bootstrap sample”
  2. E. del Barrio, C. Matrán, J. A. Cuesta-Albertos, Necessary conditions for the bootstrap of the mean of a triangular array
  3. J. A. Cuesta-Albertos, C. Matrán, The asymptotic distribution of the bootstrap sample mean of an infinitesimal array
  4. Paul Deheuvels, David M. Mason, Galen R. Shorack, Some results on the influence of extremes on the bootstrap

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