Approximations for weighted bootstrap processes with an application

Statistics and Probability Letters

Volumn 48, Issue 1, 2000, Pages 59-70

  Horváth, Lajos ^a   Kokoszka, Piotr ^b   Steinebach, Josef ^c  

^a UNIVERSITY OF UTAH   (United States)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

^c PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Best approximation; Brownian bridge; Change point detection; Weighted bootstrap* Erdos R nyi law

Indexed keywords

EID: 0006380122     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(99)00190-X     Document Type: Article

References (22)

1. Barbe, P., Bertail, P., 1995. The Weighted Bootstrap, Lecture Notes in Statistics. Springer, Heidelberg, 98.
2. Burke, M.D., 1997a. Nonparametric model checks for regression using a weighted bootstrap, preprint.
3. Burke, M.D., 1997b. Multivariate test-of-fit and uniform confidence bands using a weighted bootstrap, preprint.
4. Burke, M.D., 1998. A Gaussian bootstrap approach to estimation and tests. In: Asymptotic Methods in Probability and Statistics. Elsevier, Amsterdam.
5. Csörgo, M., Horváth, L., 1997. Limit Theorems in Change-Point Analysis. Wiley, Chichester.
6. Csörgo, M., Horváth, L., Kokoszka, P., 1999. Approximation for bootstrapped empirical processes. Proc. Amer. Math. Soc., to appear.
7. Csörgo, M., Révész, P., 1981. Strong Approximations in Probability and Statistics. Academic Press, New York.
8. Csörgo S. Limit behaviour of the empirical characteristic function. Ann. Probab. 9:1981;130-144.
9. Dvoretzky A., Kiefer J., Wolfowitz J. Asymptotic minimax character of the sample distribution functions and of the classical multinomial estimator. Ann. Math. Statist. 27:1956;642-669.
10. Efron B. Bootstrap method: another look at the jackknife. Ann. Stat. 7:1979;1-26.
11. Erdos P., Rényi A. On a new law of large numbers. J. Analyse Math. 23:1970;103-111.
12. Feuerverger A., Mureika R.A. The empirical characteristic function and its applications. Ann. Statist. 5:1977;88-97.
13. Horváth, L., 2000. Approximations for hybrids of empirical and partial sums processes. J. Stat. Planning Inf., to appear.
14. Horváth, L., Kokoszka, P., 1998. Change-point detection with non-parametric regression, preprint.
15. Horváth L., Steinebach J. On the best approximation for bootstrapped empirical processes. Statist. Probab. Lett. 41:1999;117-122.
16. Komlós J., Major P., Tusnády G. An approximation of partial sums of independent R.V.'s and the sample DF. I.Z. Wahrsch. Verw. Gebiete. 32. 111-131:1975.
17. Levin B., Kline J. The CUSUM test of homogeneity with an application in spontaneous abortion epidemiology. Statist. Med. 4:1985;469-488.
18. Lo A.Y. A large sample study of the Bayesian bootstrap. Ann. Stat. 15:1987;360-375.
19. Parzen M.I., Wei L.J., Ying Z. A resampling method based on pivotal estimating functions. Biometrika. 81:1994;341-350.
20. Petrov, V.V., 1995. Limit Theorems of Probability Theory, Clarendon Press, Oxford.
21. Rubin D.B. The Bayesian bootstrap. Ann. Stat. 9:1981;130-134.
22. Shao, J., Tu, D., 1996. The Jacknife and the Bootstrap. Springer, New York.