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, β_{3N}. 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 β_{3N}. 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.

Keywords: Cramér large deviation, saddlepoint approximations, moderate deviations, finite population, permutation tests

@article{PS_2012__16__425_0, author = {Hu, Zhishui and Robinson, John and Wang, Qiying}, title = {Tail approximations for samples from a finite population with applications to permutation tests}, journal = {ESAIM: Probability and Statistics}, pages = {425--435}, publisher = {EDP-Sciences}, volume = {16}, year = {2012}, doi = {10.1051/ps/2010027}, mrnumber = {2972501}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2010027/} }

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 PY - 2012 SP - 425 EP - 435 VL - 16 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2010027/ UR - https://www.ams.org/mathscinet-getitem?mr=2972501 UR - https://doi.org/10.1051/ps/2010027 DO - 10.1051/ps/2010027 LA - en ID - PS_2012__16__425_0 ER -

%0 Journal Article %A Hu, Zhishui %A Robinson, John %A Wang, Qiying %T Tail approximations for samples from a finite population with applications to permutation tests %J ESAIM: Probability and Statistics %D 2012 %P 425-435 %V 16 %I EDP-Sciences %U https://doi.org/10.1051/ps/2010027 %R 10.1051/ps/2010027 %G en %F PS_2012__16__425_0

Hu, Zhishui; Robinson, John; Wang, Qiying. Tail approximations for samples from a finite population with applications to permutation tests. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 425-435. doi : 10.1051/ps/2010027. http://archive.numdam.org/articles/10.1051/ps/2010027/

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