A Sub-Gaussian Berry-Esseen Theorem For the Hypergeometric Distribution
In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeometric distribution for weak convergence to a Normal limit. We establish a Berry-Esseen theorem for the Hypergeometric distribution solely under this necessary and sufficient condition. We further derive a nonuniform Berry-Esseen bound where the tails of the difference between the Hypergeometric and the Normal distribution functions are shown to decay at a sub-Gaussian rate.
This preprint was published as S.N. Lahirir, A. Chatterjee, T. Maiti, " Normal approximation to the hypergeometric distribution in nonstandard cases and a sub-Gaussian Berry–Esseen theorem," Journal of Statistical Planning and Inference (2007): 3570-3590, doi: 10.1016/j.jspi.2007.03.033.