Bootstrapping the student t-statistic

Annals of Probability

Volumn 29, Issue 4, 2001, Pages 1435-1450

  Mason, David M ^a   Shao, Qi Man ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF OREGON   (United States)

Author keywords

Bootstrap; Order statistics; Student t statistic

Indexed keywords

EID: 0035470869     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1015345757     Document Type: Article

References (13)

1. ARAUJO, A. and GINÉ, E. (1980). The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York.
2. ARCONES, M. and GINÉ, E. (1989). The bootstrap of the mean with arbitrary bootstrap sample size. Ann. Inst. H. Poincaré Probab. Statist. 25 457-481.
3. ARCONES, M. and GINÉ, E. (1991). Additions and correction to "The bootstrap of the mean with arbitrary bootstrap sample size." Ann. Inst. H. Poincaré Probab. Statist. 27 583-595.
4. ATHREYA, K. B. (1987). Bootstrap of the mean in the infinite variance case. Ann. Statist. 15 724-731.
5. CHEN, J. and RUBIN, H. (1984). A note on the behavior of sample statistics when the population mean is infinite. Ann. Probab. 12 256-261.
6. CSÖRGÖ, S. and MASON, D. M. (1989). Bootstrapping empirical functions. Ann. Statist. 17 1447-1471.
7. DEHEUVELS, P., MASON, D. M. and SHORACK, G. R. (1993). Some results on the influence of extremes on the bootstrap. Ann. Inst. H. Poincaré Probab. Statist. 29 83-103.
8. GALAMBOS, J. (1987). The Asymptotic Theory of Extreme Order Statistics, 2nd. ed. Krieger, Malabar, FL.
9. GINÉ, E., GÖTZE, F. and MASON, D. M. (1997). When is the Student t-statistic asymptotically standard normal? Ann. Probab. 25 1514-1531.
10. GINÉ, E. and ZINN, J. (1989). Necessary conditions for the bootstrap of the mean. Ann. Statist. 17 684-691.
11. HALL, P. (1990). Asymptotic properties of the bootstrap for heavy-tailed distributions. Ann. Probab. 18 1342-1360.
12. MALLER, R. A. and RESNICK, S. I. (1984). Limiting behaviour of sums and the term of maximum modulus. Proc. London Math. Soc. 49 385-422.
13. O'BRIEN, G. L. (1980). A limit theorem for sample maxima and heavy branches in Galton-Watson trees. J. Appl. Probab. 17 539-545.