Statistical inference based on a new weighted likelihood approach

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 appropriate...

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Bibliographic Details
Published in:Metrika 2021, Vol.84 (1), p.97-120
Main Authors: Majumder, Suman, Biswas, Adhidev, Roy, Tania, Bhandari, Subir Kumar, Basu, Ayanendranath
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Estimators
Mathematics and Statistics
Parameter estimation
Probability Theory and Stochastic Processes
Robustness (mathematics)
Statistical inference
Statistics
Weighting functions
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Summary: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).
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-020-00778-y