Statistical inference based on a new weighted likelihood approach

Suman Majumder (), Adhidev Biswas (), Tania Roy (), Subir Kumar Bhandari () and Ayanendranath Basu ()
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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

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 1, No 5, 97-120

Abstract: 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).

Keywords: Asymptotic efficiency; Influence function; Robustness; Robust regression; Weighted likelihood (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-020-00778-y

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