Hellinger Distance and Non-informative Priors

Abstract

This paper introduces an extension of the Jeffreys’ rule to the construction of objective priors for non-regular parametric families. A new class of priors based on Hellinger information is introduced as Hellinger priors. The main results establish the relationship of Hellinger priors to the Jeffreys’ rule priors in the regular case, and to the reference and probability matching priors for the non-regular class introduced by Ghosal and Samanta. These priors are also studied for some non-regular examples outside of this class. Their behavior proves to be similar to that of the reference priors considered by Berger, Bernardo, and Sun, however some differences are observed. For the multi-parameter case, a combination of Hellinger priors and reference priors is suggested and some examples are considered.