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December, 1977 Large Deviation Probabilities for Samples from a Finite Population
J. Robinson
Ann. Probab. 5(6): 913-925 (December, 1977). DOI: 10.1214/aop/1176995660


Let $X_n$ be the standardized mean of $s$ observations obtained by simple random sampling from the $n$ numbers $a_{n1},\cdots, a_{nn}$ and let $b_n$ be the maximum deviation of these numbers from their mean. If $b_n$ tends to zero then the distribution function of $X_n$ tends uniformly to the normal distribution function. However this approximation is not adequate at the tails of the distribution. Here we obtain limit theorems for $P(X_n > x)$ in the two cases when $x = o(b_n^{-1})$ and $x = O(b_n^{-1})$. These are related to similar results for sums of independent random variables.


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J. Robinson. "Large Deviation Probabilities for Samples from a Finite Population." Ann. Probab. 5 (6) 913 - 925, December, 1977.


Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0372.60037
MathSciNet: MR448498
Digital Object Identifier: 10.1214/aop/1176995660

Primary: 60F10
Secondary: 62G20

Keywords: Asymptotic efficiency , large deviations , limit theorems , permutation tests , sampling without replacement

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • December, 1977
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