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Robust and efficient estimation under data grouping

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  • Nan Lin
  • Xuming He

Abstract

The minimum Hellinger distance estimator is known to have desirable properties in terms of robustness and efficiency. We propose an approximate minimum Hellinger distance estimator by adapting the approach to grouped data from a continuous distribution. It is easier to compute the approximate version for either the continuous data or the grouped data. Given certain conditions on the model distribution and reasonable grouping rules, the approximate minimum Hellinger distance estimator is shown to be consistent and asymptotically normal. Furthermore, it is robust and can be asymptotically as efficient as the maximum likelihood estimator. The merit of the estimator is demonstrated through simulation studies and real data examples. Copyright 2006, Oxford University Press.

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  • Nan Lin & Xuming He, 2006. "Robust and efficient estimation under data grouping," Biometrika, Biometrika Trust, vol. 93(1), pages 99-112, March.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:1:p:99-112
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    File URL: http://hdl.handle.net/10.1093/biomet/93.1.99
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    Cited by:

    1. Zhong Guan, 2017. "Bernstein polynomial model for grouped continuous data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 831-848, October.
    2. Zhou, Wei & O'Neill, Eoghan & Moncaster, Alice & Reiner, David M. & Guthrie, Peter, 2020. "Forecasting urban residential stock turnover dynamics using system dynamics and Bayesian model averaging," Applied Energy, Elsevier, vol. 275(C).
    3. Chudamani Poudyal, 2024. "Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data," Papers 2401.14593, arXiv.org, revised Feb 2024.
    4. Chen, Shande & Manatunga, Amita K., 2007. "A note on proportional hazards and proportional odds models," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 981-988, June.

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