Estimation Efficiency under a Two-Sample Density Ratio Model

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Abstract: In many applications, we collect independent samples from interconnected populations. These population distributions share some latent structure, so it is advantageous to jointly analyze the multiple samples. Recently, many researchers have advocated the use of the semiparametric density ratio model (DRM) to account for the latent structure the multiple populations share and have developed more efficient data analysis procedures based on pooled data. In this talk, we investigate the efficiency of some estimators under a two-sample DRM. We consider the scenario where we have two samples whose sizes grow to infinity at different rates, and study the DRM-based inferences for the population corresponding to the smaller-sized sample. We theoretically prove that some DRM-based estimators achieve the same asymptotic efficiency as the parametric estimates derived under a specific parametric model. Our simulation studies on quantile estimation help to confirm our theoretical results.