A BerryEsseen theorem for hypergeometric probabilities under minimal conditions
Authors:
S. N. Lahiri and A. Chatterjee
Journal:
Proc. Amer. Math. Soc. 135 (2007), 15351545
MSC (2000):
Primary 60F05; Secondary 60G10, 62E20, 62D05.
Published electronically:
January 5, 2007
MathSciNet review:
2276664
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: In this paper, we consider simple random sampling without replacement from a dichotomous finite population and derive a necessary and sufficient condition on the finite population parameters for a valid large sample Normal approximation to Hypergeometric probabilities. We then obtain lower and upper bounds on the difference between the Normal and the Hypergeometric distributions solely under this necessary and sufficient condition.
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 Bloznelis, M. (1999). A BerryEsseen bound for finite population Student's statistic. Annals of Probability 27 20892108. MR 1742903 (2000m:62004)
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 Bloznelis, M. and Götze, F. (2000). An Edgeworth expansion for finitepopulation statistics. Bernoulli 6 729760. MR 1777694 (2001k:62010)
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 Blyth, C. R. and Staudte, R. G. (1997). Hypothesis estimates and acceptability profiles for contingency tables. Journal of the American Statistical Association 92 694699. MR 1467859
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 Lahiri, S. N., Chatterjee, A. and Maiti, T. (2004). A SubGaussian BerryEsseen Theorem for the Hypergeometric probabilities. Preprint # 200421 (posted at http://seabiscuit.stat.iastate.edu/departmental/preprint/preprint.html#2004), Iowa State University, IA (also, posted as math.PR/0602276 at http://arxiv.org).
 10.
 Nicholson, W. L. (1956). On the Normal approximation to the Hyprgeometric distribution. Annals of Mathematical Statistics 27 471483. MR 0087246 (19:326c)
 11.
 Madow, W. G. (1948). On the limiting distributions of estimates based on samples from finite universes. Annals of Mathematical Statistics 19 535545. MR 0029136 (10:554a)
 12.
 Patel, J. K. and Samaranayake, V. A. (1991). Prediction intervals for some discrete distributions. Journal of Quality Technology 23 270278.
 13.
 Seber, G. A. F. (1970). The effects of trap response on tag recapture estimates. Biometrics 26 1322.
 14.
 Sohn, S. Y. (1997). Accelerated lifetests for intermittent destructive inspection, with logistic failuredistribution. IEEE Transactions on Reliability 46 1221295.
 15.
 Wendell, J. P. and Schmee, J. (1996). Exact inference for proportions from a stratified finite population. Journal of the American Statistical Association 91 825830. MR 1395749 (97a:62022)
 16.
 Wittes, J. T. (1972). On the bias and estimated variance of Chapman's twosample capturerecapture population estimate. Biometrics 28 592597.
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Additional Information
S. N. Lahiri
Affiliation:
Department of Statistics, Iowa State University, Ames, Iowa 50011
Address at time of publication:
Department of Statistics, Texas A&M University, College Station, Texas 77843
Email:
snlahiri@iastate.edu
A. Chatterjee
Affiliation:
Department of Statistics, Iowa State University, Ames, Iowa 50011
Address at time of publication:
Department of Statistics, Texas A&M University, College Station, Texas 77843
Email:
cha@iastate.edu
DOI:
http://dx.doi.org/10.1090/S0002993907086765
PII:
S 00029939(07)086765
Received by editor(s):
April 12, 2005
Received by editor(s) in revised form:
February 16, 2006
Published electronically:
January 5, 2007
Additional Notes:
This research was partially supported by NSF grant no. DMS 0306574.
Communicated by:
Edward C. Waymire
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
