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.
Publié le : 1977-12-14
Classification:
Large deviations,
limit theorems,
asymptotic efficiency,
sampling without replacement,
permutation tests,
60F10,
62G20
@article{1176995660,
author = {Robinson, J.},
title = {Large Deviation Probabilities for Samples from a Finite Population},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 913-925},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995660}
}
Robinson, J. Large Deviation Probabilities for Samples from a Finite Population. Ann. Probab., Tome 5 (1977) no. 6, pp. 913-925. http://gdmltest.u-ga.fr/item/1176995660/