Abstract
Suppose that $U$ is a $U$-statistic of degree 2 based on a simple random sample of size $n$ selected without replacement from a finite population of $N$ elements. A bound for the difference between the distribution function of a standardized version of $U$ and its single-term Edgeworth expansion is given. We apply these results to obtain an Edgeworth expansion for the variance estimator in a finite population. Some simulation results are reported in this case.
Citation
P. N. Kokic. N. C. Weber. "An Edgeworth Expansion for $U$-Statistics Based on Samples from Finite Populations." Ann. Probab. 18 (1) 390 - 404, January, 1990. https://doi.org/10.1214/aop/1176990955
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