Abstract: The potential use of auxiliary summary information to improve the efficiency of estimation has attracted significant interest. Most existing methods assume that the data distribution is the same for the sample data and for the population that generates the auxiliary information. However, recent works have relaxed this assumption by allowing heterogeneity between the two covariate distributions. We consider an empirical likelihood approach that guarantees that using auxiliary information will increase the efficiency of estimation when the variability associated with this information is sufficiently small. We also investigate the effects of this variability on the efficiency. Furthermore, we implement the proposed approach using a Newton-Raphson-type algorithm. Lastly, we discuss our simulation results, which demonstrate the efficiency gains and confirm the large sample approximations.

Key words and phrases: Auxiliary information, data integration, empirical likelihood, estimation efficiency, information uncertainty, summary information.