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Non-iterative Estimation Update for Parametric and Semiparametric Models with Population-based Auxiliary Information
With the advancement in disease registries and surveillance data, population-based information on disease incidence, survival probability or other important biological characteristics become increasingly available. Such information can be leveraged in studies that collect detailed measurements but with smaller sample sizes. In contrast to recent proposals that formulate the additional information as constraints in optimization problems, we develop a general framework to construct simple estimators that update the usual regression estimators with some functionals of data that incorporate the additional information. We consider general settings which include nuisance parameters in the auxiliary information, non-i.i.d. data such as case-control sampling, and semiparametric models with infinite dimensional parameters. Detailed examples of several important data and sampling settings are provided.