On Edgeworth Expansions in Generalized Urn Models
arXiv:1401.4419 · doi:10.1007/s10959-012-0454-z
Abstract
The random vector of frequencies in a generalized urn model is viewed as conditionally independent random variables, given their sum. Such a representation is exploited to derive Edgeworth expansions for a sum of functions of such frequencies. Applying these results to urn models such as with- and without-replacement sampling schemes as well as the multicolor Polya-Egenberger model, new results are obtained for the chi-square statistic, for the sample sum in a without replacement scheme, and for the so-called Dixon statistic that is useful in comparing two samples.
Journal of Theoretical Probability. 2012