ON THE ASYMPTOTIC EQUIVALENCE OF HELLINGER DISTANCE AND KULLBACK-LEIBLER LOSS
Yuichiro Kanazawa, Atsuyuki Kogure, Sang-Gil Lee · JOURNAL OF THE JAPAN STATISTICAL SOCIETY · 1999
Hellinger distance, Kullback-Leibler loss, and variance-stabilizing integrated square error are shown to be asymptotically equivalent up to a constant. Simulation confirmed the result. Implications of the result for dernel and histogram density estimation and the connection of the result with goodness of fit tests are discussed.