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Statistical inference based on a new weighted likelihood approach

Author

Listed:
  • Suman Majumder

    (North Carolina State University)

  • Adhidev Biswas

    (Indian Statistical Institute)

  • Tania Roy

    (Novartis Healthcare Private Limited)

  • Subir Kumar Bhandari

    (Indian Statistical Institute)

  • Ayanendranath Basu

    (Indian Statistical Institute)

Abstract

We discuss a new weighted likelihood method for robust parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is correctly specified. This is achieved by appropriately weighting the score function at each observation in the maximum likelihood score equation. The weight function determines the compatibility of each observation with the model in relation to the remaining observations and applies a downweighting only if it is necessary, rather than automatically downweighting a proportion of the observations all the time. This allows the estimators to retain full asymptotic efficiency at the model. We establish all the theoretical properties of the proposed estimators and substantiate the theory developed through simulation and real data examples. Our approach provides an alternative to the weighted likelihood method of Markatou et al. (J Stat Plan Inference 57(2):215–232, 1997; J Am Stat Assoc 93(442):740–750, 1998).

Suggested Citation

  • Suman Majumder & Adhidev Biswas & Tania Roy & Subir Kumar Bhandari & Ayanendranath Basu, 2021. "Statistical inference based on a new weighted likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 97-120, January.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:1:d:10.1007_s00184-020-00778-y
    DOI: 10.1007/s00184-020-00778-y
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    References listed on IDEAS

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    1. Agostinelli, Claudio, 2002. "Robust model selection in regression via weighted likelihood methodology," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 289-300, February.
    2. Agostinelli, Claudio & Markatou, Marianthi, 1998. "A one-step robust estimator for regression based on the weighted likelihood reweighting scheme," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 341-350, March.
    3. 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.
    4. Agostinelli, Claudio, 2007. "Robust estimation for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5867-5875, August.
    5. C. Agostinelli, 2002. "Robust stepwise regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(6), pages 825-840.
    6. Christian Léger & Joseph Romano, 1990. "Bootstrap choice of tuning parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 709-735, December.
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