Weighted Likelihood Equations with Bootstrap Root Search

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Abstract
We discuss a method of weighting likelihood equations with the aim of obtaining fully efficient and robust estimators. We discuss the case of continuous probability models using unimodal weighting functions. These weighting functions downweight observations that are inconsistent with the assumed model. At the true model, therefore, the proposed estimating equations behave like the ordinary likelihood equations. We investigate the number of solutions of the estimating equations via a bootstrap root search; the estimators obtained are consistent and asymptotically normal and have desirable robustness properties. An extensive simulation study and real data examples illustrate the operating characteristics of the proposed methodology.

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