On bootstrap estimation of the distribution of the studentized mean

Annals of the Institute of Statistical Mathematics

Volumn 48, Issue 3, 1996, Pages 403-421

  Hall, Peter ^a   Lepage, Raoul ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Bootstrap; Central limit theorem; Consistency; Domain of attraction; Domain of partial attraction; Heavy tail; Percentile t method; Self normalization; Stable law; Studentization

Indexed keywords

EID: 0013252196     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00050845     Document Type: Article

References (16)

1. Arcones, M. A. and Giné, E. (1989). The bootstrap of the mean with arbitrary sample size, Ann. Inst. Henri Poincaré Ser. B, 25, 457-481.
2. Arcones, M. A. and Giné, E. (1991). Additions and corrections to the bootstrap of the mean with arbitrary sample size, Ann. Inst. Henri Poincaré Ser. B, 27, 583-595.
3. Athreya, K. B. (1987). Bootstrap of the mean in the infinite variance case, Ann. Statist., 15, 724-731.
4. Deheuvels, P., Mason, D. M. and Shorack, G. R. (1993). Some results on the influence of extremes on the bootstrap, Ann. Inst. Henri Poincaré Ser. B, 29, 83-103.
5. Giné, E. and Zinn, J. (1989). Necessary conditions for the bootstrap of the mean, Ann. Statist., 17, 684-691.
6. Hall, P. (1990a). Asymptotic properties of the bootstrap for heavy-tailed distributions, Ann. Probab., 18, 1342-1360.
7. Hall, P. (1990b). Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems, J. Multivariate Anal., 32, 177-203.
8. Hall, P. (1992). The Bootstrap and Edgeworth Expansion, Springer, New York.
9. Knight, K. (1989). On the bootstrap of the sample mean in the infinite variance case, Ann. Statist., 17, 1168-1175.
10. Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional, Biometrika, 75, 237-249.
11. Owen, A. B. (1990). Empirical likelihood confidence regions, Ann. Statist., 18, 90-120.
12. Petrov, V. V. (1975). Sums of Independent Random Variables, Springer, Berlin.
13. Politis, D. N. and Romano, J. P. (1994). Large sample confidence regions based on subsamples under minimal assumptions, Ann. Statist., 22, 2031-2050.
14. Pollard, D. (1984). Convergence of Stochastic Processes, Springer, New York.
15. Swanepoel, J. W. H. (1986). A note on proving that the (modified) bootstrap works, Comm. Statist. Theory Methods, 15, 3193-3203.
16. Wu, C. F. J. (1990). On the asymptotic properties of the jackknife histogram, Ann. Statist., 18, 1438-1452.