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On the asymptotics of minimum disparity estimation

Author

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  • Arun Kumar Kuchibhotla

    (University of Pennsylvania)

  • Ayanendranath Basu

    (Indian Statistical Institute)

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.

Suggested Citation

  • Arun Kumar Kuchibhotla & Ayanendranath Basu, 2017. "On the asymptotics of minimum disparity estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 481-502, September.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-016-0520-4
    DOI: 10.1007/s11749-016-0520-4
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    References listed on IDEAS

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    1. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    2. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    3. Kuchibhotla, Arun Kumar & Basu, Ayanendranath, 2015. "A general set up for minimum disparity estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 68-74.
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