Tail approximations for samples from a finite population with applications to permutation tests

Zhishui Hu; John Robinson; Qiying Wang

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 425-435
  • ISSN: 1292-8100

Abstract

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This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions on the sampled population and an error term depending only on β3N. Application to permutation tests is investigated giving a new limit result for the tail conditional probability of the statistic given order statistics under mild conditions. Some numerical results are given to illustrate the accuracy of the approximation by comparing our results to saddlepoint approximations requiring strong conditions.

How to cite

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Hu, Zhishui, Robinson, John, and Wang, Qiying. "Tail approximations for samples from a finite population with applications to permutation tests." ESAIM: Probability and Statistics 16 (2012): 425-435. <http://eudml.org/doc/222451>.

@article{Hu2012,
abstract = {This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions on the sampled population and an error term depending only on β3N. Application to permutation tests is investigated giving a new limit result for the tail conditional probability of the statistic given order statistics under mild conditions. Some numerical results are given to illustrate the accuracy of the approximation by comparing our results to saddlepoint approximations requiring strong conditions.},
author = {Hu, Zhishui, Robinson, John, Wang, Qiying},
journal = {ESAIM: Probability and Statistics},
keywords = {Cramér large deviation; saddlepoint approximations; moderate deviations; finite population; permutation tests},
language = {eng},
month = {8},
pages = {425-435},
publisher = {EDP Sciences},
title = {Tail approximations for samples from a finite population with applications to permutation tests},
url = {http://eudml.org/doc/222451},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Hu, Zhishui
AU - Robinson, John
AU - Wang, Qiying
TI - Tail approximations for samples from a finite population with applications to permutation tests
JO - ESAIM: Probability and Statistics
DA - 2012/8//
PB - EDP Sciences
VL - 16
SP - 425
EP - 435
AB - This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions on the sampled population and an error term depending only on β3N. Application to permutation tests is investigated giving a new limit result for the tail conditional probability of the statistic given order statistics under mild conditions. Some numerical results are given to illustrate the accuracy of the approximation by comparing our results to saddlepoint approximations requiring strong conditions.
LA - eng
KW - Cramér large deviation; saddlepoint approximations; moderate deviations; finite population; permutation tests
UR - http://eudml.org/doc/222451
ER -

References

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  10. Z. Hu, J. Robinson and Q. Wang, Crameŕ-type large deviations for samples from a finite population. Ann. Statist.35 (2007) 673–696.  
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  12. J. Robinson, An asymptotic expansion for samples from a finite population. Ann. Statist.6 (1978) 1004–1011.  
  13. J. Robinson, Saddlepoint approximations for permutation tests and confidence intervals. J. R. Statist. Soc. B20 (1982) 91–101.  
  14. J. Robinson, T. Hoglund, L. Holst and M.P. Quine, On approximating probabilities for small and large deviations in Rd. Ann. Probab.18 (1990) 727–753.  
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