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Edgeworth Expansions for a Sample Sum from a Finite Set of Independent Random Variables

   
@article{EJP447,
	author = {Zhishui Hu and John Robinson and Qiying Wang},
	title = {Edgeworth Expansions  for a Sample Sum from a Finite Set of Independent Random Variables},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {12},
	year = {2007},
	keywords = {Edgeworth expansion, finite population, sampling without replacement.},
	abstract = {Let $\{X_1,\cdots ,X_N\}$ be a set of $N$  independent random variables, and let $S_n$ be a sum of $n$ random  variables chosen without replacement from the set $\{X_1, \cdots ,  X_N\}$ with equal probabilities.  In this paper we give a one-term  Edgeworth expansion of the remainder term for the normal  approximation of $S_n$ under   mild conditions.},
	pages = {no. 52, 1402-1417},
	issn = {1083-6489},
	doi = {10.1214/EJP.v12-447},    
        url = {http://ejp.ejpecp.org/article/view/447}}