Inference procedures based on the minimization of divergences are popular
statistical tools. Beran (Ann stat 5(3):445–463, 1977) proved consistency and asymp-
totic normality of the minimum Hellinger distance (MHD) estimator. This method
was later extended to the large class of disparities in discrete models by Lindsay (Ann
stat 22(2):1081–1114, 1994) who proved existence of a sequence of roots of the esti-
mating equation which is consistent and asymptotically normal. However, the current
literature does not provide a general asymptotic result about the minimizer of a generic
disparity. In this paper, we prove, under very general conditions, an asymptotic rep-
resentation of the minimum disparity estimator itself (and not just for a root of the
estimating equation), thus generalizing the results of Beran (Ann stat 5(3):445–463,
1977) and Lindsay (Ann stat 22(2):1081–1114, 1994). This leads to a general frame-
work for m

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• On the asymptotics of minimum disparity estimation