On the Le Cam Distance Between Multivariate Hypergeometric and Multivariate Normal Experiments

In this short note, we develop a local approximation for the log-ratio of multivariate hypergeometric probability mass function over corresponding multinomial function. conjunction with bounds from Carter (Ann Stat 30(3):708–730, 2002) and Ouimet (J Plan Inference 215:218–233, 2021) on total variation between law vector jittered by uniform $$(-\,1/2,1/2)^d$$ normal distribution, expansion is then used to obtain bound random distribution. As corollary, find an upper Le Cam distance experiments.