On the asymptotics of minimum disparity estimation

Arun Kumar Kuchibhotla () and Ayanendranath Basu ()
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Arun Kumar Kuchibhotla: University of Pennsylvania
Ayanendranath Basu: Indian Statistical Institute

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 3, No 2, 502 pages

Abstract: Abstract Inference procedures based on the minimization of divergences are popular statistical tools. Beran (Ann stat 5(3):445–463, 1977) 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 Lindsay (Ann stat 22(2):1081–1114, 1994) 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 (Ann stat 5(3):445–463, 1977) and Lindsay (Ann stat 22(2):1081–1114, 1994). This leads to a general framework for minimum disparity estimation encompassing both discrete and continuous models.

Keywords: Disparity; Quadratic approximation; Non-parametric density estimation; 62F12; 62F35 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11749-016-0520-4

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