Biased-sample empirical likelihood weighting for missing data problems: an alternative to inverse probability weighting

Abstract Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW that estimator can be remarkably unstable if some probabilities very close zero. To overcome this problem, at least three remedies have been developed literature: stabilizing, thresholding, and trimming. However, final estimators still IPW-type estimators, inevitably inherit certain weaknesses naive estimator: they may biased. We propose a biased-sample empirical likelihood (ELW) method serve same general purpose as IPW, while completely overcoming instability by circumventing inverse probabilities. The ELW weights always well defined easy implement. show theoretically asymptotically normal more efficient than its stabilized version for missing problems. Our simulation results real analysis indicate shift-equivariant, nearly unbiased, usually outperforms terms mean square error.