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On the asymptotics of minimum disparity estimation. (English) Zbl 1380.62102

Summary: Inference procedures based on the minimization of divergences are popular statistical tools. In [Ann. Stat. 5, 445–463 (1977; Zbl 0381.62028)], R. Beran proved consistency and asymptotic normality of the minimum Hellinger distance (MHD) estimator. This method was later extended to the large class of disparities in discrete models by B. G. Lindsay [ibid. 22, No. 2, 1081–1114 (1994; Zbl 0807.62030)] who proved existence of a sequence of roots of the estimating 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 representation of the minimum disparity estimator itself (and not just for a root of the estimating equation), thus generalizing the results of Beran [loc. cit.] and Lindsay [loc. cit.]. This leads to a general framework for minimum disparity estimation encompassing both discrete and continuous models.

MSC:

62F12 Asymptotic properties of parametric estimators
62F10 Point estimation
62F35 Robustness and adaptive procedures (parametric inference)
62G07 Density estimation
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