Resampling: Consistency of substitution estimators

Annals of Statistics

Volumn 24, Issue 6, 1996, Pages 2297-2318

  Putter, Hein ^a   Van Zwet, Willem R ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Bootstrap; Consistency; Equicontinuity; Local uniform convergence; Resampling; Set of first category; Substitution estimator

Indexed keywords

EID: 0030344229     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032181156     Document Type: Article

References (15)

1. BERAN, R. J. (1982). Estimated sampling distributions: the bootstrap and competitors. Ann. Statist. 10 212-225,
2. BERAN, R. J. (1984). Bootstrap methods in statistics. Jber. Deutsch. Math.-Verein. 86 14-30.
3. BICKEL, P. J. and FREEDMAN, D. A. (1981). Some asymptotic theory for the bootstrap. Ann. Statist. 9 1196-1217.
4. BILLINGSLEY, P. (1986). Convergence of Probability Measures. Wiley, New York.
5. BIRGÉ, L. (1983). Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahrsch. Verw. Gebiete 65 181-237.
6. BIRGÉ, L. (1986). On estimating a density using Hellinger distance and some other strange facts. Probab. Theory Related Fields 71 271-291.
7. DUDLEY, R. M. (1989). Real Analysis and Probability. Wadsworth, Belmont, CA.
8. LE CAM, L. M. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates. University of California Publications in Statistics 1 277-330.
9. LE CAM, L. M. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 1 38-53.
10. LE CAM, L. M. (1986). Asymptotic Methods in Statistical Decision Theory. Springer, New York.
11. LE CAM, L. M. and YANG, G. L. (1990). Asymptotics in Statistics: Some Basic Concepts. Springer, New York.
12. POLITIS, D. and ROMANO, J. (1994). Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist. 22 2031-2050.
13. PUTTER, H. (1994). Consistency of resampling methods. Ph.D. thesis, Univ. Leiden.
14. PUTTER, H. and VAN ZWET, W. R. (1996). On a set of the first category. In Festschrift for Lucien Le Cam. Springer, New York. To appear.
15. VAN ZWET, W. R. (1996). Resampling: the jackknife and the naïve bootstrap. Unpublished manuscript.