Some results on the influence of extremes on the bootstrap

 Access to full text

 Full (PDF)

1. [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. Zbl0712.62015MR1045246
2. [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. Zbl0747.62019MR1141249
3. [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. [4] K.B. Athreya, Bootstrap of the Mean in the Infinite Variance Case, Ann. Statist., Vol. 15, 1987, pp. 724-731. Zbl0628.62042MR888436
5. [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. Zbl0313.62020MR405537
6. [6] D.J. Bickel and D.A.: Freedman, Some Asymptotic Theory for the Bootstrap, Ann. Statist., Vol. 9, 1981, pp. 1196-1217. Zbl0449.62034MR630103
7. [7] J. Brétagnolle, Lois Limites du Bootstrap de Certaines Fonctionnelles, Ann. Inst. Henri Poincaré, Vol. 19, 1983, pp. 281-296. Zbl0535.62046MR725561
8. [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. Zbl0589.60030MR815961
9. [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. Zbl0572.60028MR835156
10. [10] S. Csörgö, E. Haeusler and D.M. Mason, The Asymptotic Distribution of Trimmed Sums, Ann. Probab., Vol. 16, 1988 a, pp. 672-699. Zbl0647.62030MR929070
11. [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. Zbl0657.60029MR956558
12. [12] P. Deheuvels and D.M. Mason, Bahadur-Kiefer-type Processes, Ann. Probab., Vol. 18, 1990, pp. 669-697. Zbl0712.60028MR1055427
13. [13] J.H.J. Einmahl and D.M. Mason, Strong Limit Theorems for Weighted Quantile Processes, Ann. Probab., Vol. 16, 1988, pp. 1623-1633. Zbl0659.60052MR958207
14. [14] P. Griffin and W.E. Pruitt, Asymptotic Normality and Subsequential Limits of Trimmed Sums, Ann. Probab., Vol. 17, 1989, pp. 1186-1219. Zbl0688.60016MR1009452
15. [15] L. de Haan, On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Mathematical Centre Tracts, Amsterdam, 1971. Zbl0226.60039
16. [16] P. Hall, Asymptotic Properties of the Bootstrap for Heavy Tailed Distributions, Ann. Statist., Vol. 18, 1990, pp. 1342-1360. Zbl0714.62035MR1062071
17. [17] B.R. James, A Functional Law of the Iterated Logarithm for Empirical Distributions, Ann. Probab., Vol. 3, 1975, pp. 763-772. Zbl0347.60030MR402881
18. [18] J. Kiefer, Deviations Between the Sample Quantile Process and the Sample D.F., In: Nonparametric Techniques in Statistical Inference, M. PURI, Ed., Press, London1970, pp. 299-319, Cambridge Univ. MR277071
19. [19] K. Knight, On the Bootstrap of the Sample Mean in the Infinite Variance Case, Ann. Statist., Vol. 17, 1989, pp. 1168-1175. Zbl0687.62017MR1015144
20. [20] D.M. Mason, The Asymptotic Distribution of Weighted Empirical Distributions, Stochastic Processes, Appl., Vol. 15, 1983, pp. 99-109. Zbl0504.62021MR694539
21. [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. Zbl0638.60040MR893903
22. [22] N. O'Reilly, On the Weak Convergence of Empirical Processes in Sup-Norm Metrics, Ann. Probab., Vol. 2, 1974, pp. 642-651. Zbl0301.60007
23. [23] G. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986. Zbl1170.62365MR838963
24. [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. Zbl0724.60020MR1117278
25. [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. [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. Zbl0623.62041MR860478

1. J. A. Cuesta-Albertos, C. Matrán, The asymptotic distribution of the bootstrap sample mean of an infinitesimal array