Statistical Inference Based on a New Weighted Likelihood Approach

TL;DR

This paper introduces a new weighted likelihood estimation method that achieves robustness against model misspecification while maintaining full efficiency when the model is correct, supported by theoretical analysis and empirical validation.

Contribution

It proposes a novel weighted likelihood approach that adaptively downweights observations, offering a robust and efficient alternative to existing methods.

Findings

The estimator is fully efficient under correct model specification.

The method demonstrates robustness through simulations and real data examples.

Theoretical properties of the estimator are rigorously established.

Abstract

We discuss a new weighted likelihood method for 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. (1997, 1998).