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Edgeworth expansions for a sample sum from a finite set of independent random variables
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Zhishui Hu, University of Science and Technology of China
John Robinson, The University of Sydney
Qiying Wang, The University of Sydney
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Abstract
Let X1,...,XN be a set of N
independent random variables, and let Sn be a sum of n random
variables chosen without replacement from the set {X1,...,XN} with equal probabilities. In this paper we give a one-term
Edgeworth expansion of the remainder term for the normal
approximation of Sn under
mild conditions.
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Full text: PDF
Pages: 1402-1417
Published on: November 4, 2007
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Bibliography
-
Babu, G. J. and Bai, Z. D. (1996). Mixtures of global and local
Edgeworth expansions and their applications. J. Multivariate.
Anal. 59 282-307.
MR1423736 (98d:62023)
-
von Bahr, B. (1972). On sampling
from a finite set of independent random variables.
Z. Wahrsch. Verw. Geb. 24 279--286.
MR0331471 (48 #9804)
-
Bhattacharya, R. N. and Ranga Rao, R. (1976). Normal approximation and
asymptotic expansions. Wiley, New York.
MR0436272 (55 #9219)
-
Bickel, P. J. and von Zwet, W. R. (1978). Asymptotic expansions for the
power of distribution-free tests in the two-sample problem.
Ann. Statist. 6 937-1004.
MR0499567 (80j:62043)
-
Bikelis, A. (1969). On the estimation of the remainder term in the central
limit theorem for samples from finite populations. Studia
Sci. Math. Hungar. 4 345-354 (in Russian).
MR0254902 (40 #8109)
-
Bloznelis, M. (2000a). One and two-term Edgeworth expansion for finite population
sample mean. Exact results, I. Lith. Math. J. 40(3)
213-227.
MR1803645 (2001k:62011)
-
Bloznelis, M. (2000b). One and two-term Edgeworth expansion for finite population
sample mean. Exact results, II. Lith. Math. J. 40(4)
329-340.
MR1819377 (2002d:62007)
-
Bloznelis, M. (2003). Edgeqorth expansions for studentized versions of
symmetric finite population statistics. Lith. Math. J.
43(3) 221-240.
MR2019541 (2004h:62019)
-
Bloznelis, M. and G"otze, F. (2000).
An Edgeworth expansion for finite population $U$-statistics.
Bernoulli 6 729-760.
MR1777694 (2001k:62010)
-
Bloznelis, M. and G"otze, F. (2001). Orthogonal decomposition of finite population
statistic and its applications to distributional asymptotics.
Ann. Statist. 29 899-917.
MR1865345 (2002h:62029)
-
Erd"os, P. and Renyi, A. (1959). On the central limit theorem for
samples from a finite population. Fubl. Math. Inst. Hungarian
Acad. Sci. 4 49-61.
MR0107294 (21 #6019)
-
H"oglund, T.(1978). Sampling from a finite population. A remainder
term estimate. Scand. J. Statistic. 5 69-71.
MR0471130 (57 #10868)
-
Kokic, P. N. and Weber, N. C. (1990). An Edgeworth
expansion for $U$-statistics based on samples from finite
populations.
Ann. Probab. 18 390-404.
MR1043954 (91e:60068)
-
Mirakjmedov, S. A. (1983). An asymptotic expansion for
a sample sum from a finite sample.
Theory Probab. Appl. 28(3) 492-502.
-
Nandi, H. K. and Sen, P. K. (1963).
On the properties of $U$-statistics when the observations are not
independent II: unbiased estimation of the parameters of a finite
population. Calcutta Statist. Asso. Bull 12 993-1026.
MR0161418 (28 #4624b)
-
Robinson, J. (1978). An asymptotic expansion for samples from a
finite population. Ann. Statist. 6 1004-1011.
MR0499568 (80i:62016)
-
Schneller, W. (1989).
Edgeworth expansions for linear rank statistics. Ann.
Statist. 17 1103--1123.
MR1015140 (90k:62043)
-
Zhao, L.C. and Chen, X. R. (1987).
Berry-Esseen bounds for finite population $U$-statistics.
Sci. Sinica. Ser. A 30 113-127.
MR0892467 (88k:60048)
-
Zhao, L.C. and Chen, X. R. (1990).
Normal approximation for finite population $U$-statistics.
Acta Math. Appl. Sinica 6 263-272.
MR1078067 (92a:60070)
-
Zhao, L.C., Wu, C. Q. and Wang, Q. (2004).
Berry-Esseen bound for a sample sum from a finite set of
independent random variables. J. Theoretical Probab.
17 557-572.
MR2091551 (2005i:60035)
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Electronic Journal of Probability. ISSN: 1083-6489 |
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