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Approximation for bootstrapped empirical processes
Author(s):
Miklós
Csörgo;
Lajos
Horváth;
Piotr
Kokoszka
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2457-2464.
MSC (1991):
Primary 62G30;
Secondary 62G07.
Posted:
November 29, 1999
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Abstract:
We obtain an approximation for the bootstrapped empirical process with the rate of the Komlós, Major and Tusnády approximation for empirical processes. The proof of the new approximation is based on the Poisson approximation for the uniform empirical distribution function and the Gaussian approximation for randomly stopped sums.
References:
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- 2.
- Csörg\H{o}, M., Csörg\H{o}, S., Horváth, L. and Mason, D. M. (1986). Weighted empirical and quantile processes. Ann. Probab. 14 31-85. MR 87e:60041
- 3.
- Csörg\H{o}, M., P. Deheuvels, and Horváth, L. (1987). An approximation of stopped sums with applications in queueing theory. Adv. Appl. Prob. 19 674-690. MR 89c:60045
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- Csörg\H{o}, M., and Horváth, L. (1993). Weighted Approximations in Probability and Statistics. Wiley, Chichester. MR 94c:60060
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Additional Information:
Miklós
Csörgo
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa Ontario, Canada K1S 5B6
Lajos
Horváth
Affiliation:
Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, Utah 84112-0090
Email:
horvath@math-utah.edu
Piotr
Kokoszka
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom
DOI:
10.1090/S0002-9939-99-05409-X
PII:
S 0002-9939(99)05409-X
Keywords:
Bootstrap,
empirical process,
Poisson process,
Brownian bridge,
approximations
Received by editor(s):
September 16, 1998
Posted:
November 29, 1999
Additional Notes:
The first author's research was supported by an NSERC Canada grant
The second author's research was supported by NATO grant CRG 960 503
Dedicated:
In memory of Béla Szokefalvi--Nagy
Communicated by:
Wei Y. Loh
Copyright of article:
Copyright
2000,
American Mathematical Society
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