Some results on the influence of extremes on the bootstrap
Deheuvels, Paul ; Mason, David M. ; Shorack, Galen R.
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993), p. 83-103 / Harvested from Numdam
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@article{AIHPB_1993__29_1_83_0,
     author = {Deheuvels, Paul and Mason, David M. and Shorack, Galen R.},
     title = {Some results on the influence of extremes on the bootstrap},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {29},
     year = {1993},
     pages = {83-103},
     mrnumber = {1204519},
     zbl = {0774.62042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1993__29_1_83_0}
}

Deheuvels, Paul; Mason, David M.; Shorack, Galen R. Some results on the influence of extremes on the bootstrap. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) pp. 83-103. http://gdmltest.u-ga.fr/item/AIHPB_1993__29_1_83_0/

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

[2] M.A. Arcones and E. Giné, Additions and Corrections to the Bootstrap of the Mean with Arbitrary Bootrstrap Sample Size, Ann. Inst. Henri Poincaré, Vol. 27, 1992, pp. 583-595. | Numdam | MR 1141249 | Zbl 0747.62019

[3] K.B. Athreya, Bootstrap for the Mean in the Infinite Variance Case II, Technical Report 86-21, Dept. of Statistics, Iowa State University, 1985.

[4] K.B. Athreya, Bootstrap of the Mean in the Infinite Variance Case, Ann. Statist., Vol. 15, 1987, pp. 724-731. | MR 888436 | Zbl 0628.62042

[5] A. Balkema and L. De Haan, Limit Laws for Order Statistics, In: Colloq. Math. Soc. János Bolyai. Limit' Theorems of Probability, P. RÉVÉSZ Ed., North Holland, Amsterdam, Vol. 11, 1975, pp. 17-22. | MR 405537 | Zbl 0313.62020

[6] D.J. Bickel and D.A.: Freedman, Some Asymptotic Theory for the Bootstrap, Ann. Statist., Vol. 9, 1981, pp. 1196-1217. | MR 630103 | Zbl 0449.62034

[7] J. Brétagnolle, Lois Limites du Bootstrap de Certaines Fonctionnelles, Ann. Inst. Henri Poincaré, Vol. 19, 1983, pp. 281-296. | Numdam | MR 725561 | Zbl 0535.62046

[8] M. Csörgö, S. Csörgö, L. Horváth and D.M. Mason, Normal and Stable Convergence of Integral Functions of the Empirical Distribution Function, Ann. Probab., Vol. 14, 1986, pp. 86-118. | MR 815961 | Zbl 0589.60030

[9] S. Csörgö, L. Horváth and D.M. Mason, What Portion of the Sample Partial Sum Asymptotically Stable or Normal? Probab. Theory Related Fields, Vol. 72, 1986, pp. 1-16. | MR 835156 | Zbl 0572.60028

[10] S. Csörgö, E. Haeusler and D.M. Mason, The Asymptotic Distribution of Trimmed Sums, Ann. Probab., Vol. 16, 1988 a, pp. 672-699. | MR 929070 | Zbl 0647.62030

[11] S. Csörgö, E. Haeusler and D.M. Mason, A Probabilistic Approach to the Asymptotic Distribution of Sums of Independent, Identically Distributed Random Variables, Adv. in Appl. Math., Vol. 9, 1988 b, pp. 259-333. | MR 956558 | Zbl 0657.60029

[12] P. Deheuvels and D.M. Mason, Bahadur-Kiefer-type Processes, Ann. Probab., Vol. 18, 1990, pp. 669-697. | MR 1055427 | Zbl 0712.60028

[13] J.H.J. Einmahl and D.M. Mason, Strong Limit Theorems for Weighted Quantile Processes, Ann. Probab., Vol. 16, 1988, pp. 1623-1633. | MR 958207 | Zbl 0659.60052

[14] P. Griffin and W.E. Pruitt, Asymptotic Normality and Subsequential Limits of Trimmed Sums, Ann. Probab., Vol. 17, 1989, pp. 1186-1219. | MR 1009452 | Zbl 0688.60016

[15] L. De Haan, On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Mathematical Centre Tracts, Amsterdam, 1971. | Zbl 0226.60039

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

[17] B.R. James, A Functional Law of the Iterated Logarithm for Empirical Distributions, Ann. Probab., Vol. 3, 1975, pp. 763-772. | MR 402881 | Zbl 0347.60030

[18] J. Kiefer, Deviations Between the Sample Quantile Process and the Sample D.F., In: Nonparametric Techniques in Statistical Inference, M. PURI, Ed., Press, London 1970, pp. 299-319, Cambridge Univ. | MR 277071

[19] K. Knight, On the Bootstrap of the Sample Mean in the Infinite Variance Case, Ann. Statist., Vol. 17, 1989, pp. 1168-1175. | MR 1015144 | Zbl 0687.62017

[20] D.M. Mason, The Asymptotic Distribution of Weighted Empirical Distributions, Stochastic Processes, Appl., Vol. 15, 1983, pp. 99-109. | MR 694539 | Zbl 0504.62021

[21] D.M. Mason and W.R. Van Zwet, A Refinement of the KMT Inequality for the Uniform Empirical Process, Ann. Probab., Vol. 15, 1987, pp. 871-884. | MR 893903 | Zbl 0638.60040

[22] N. O'Reilly, On the Weak Convergence of Empirical Processes in Sup-Norm Metrics, Ann. Probab., Vol. 2, 1974, pp. 642-651. | Zbl 0301.60007

[23] G. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986. | MR 838963 | Zbl 1170.62365

[24] G. Shorack, Some Results for Linear Combinations, In: Sums, Trimmed Sums, and Extremes, M. G. HAHN, D. M. MASON and D. C. WEINER Eds., 1991 a, pp. 377-392, Progress in Probability, Birkhäuser, Boston, Vol. 23. | MR 1117278 | Zbl 0724.60020

[25] G. Shorack, Uniform. CLT, WLLN, LIL and a Data Analytic Approach to Trimmed L-Statistics, Dept. of Statistics Technical Report, University of Washington, 1991 b.

[26] J.W.H. Swanepoel, A Note in Proving that the (Modified) Bootstrap Works, Commun. Statist. Theory Meth., Vol. 15, (11), 1986, pp. 3193-3203. | MR 860478 | Zbl 0623.62041