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Data analysis based on information from different sources, typically known as the data fusion problem, is common in economic and biomedical studies. An interesting question concerns the regression of an outcome variable on certain covariates when combining two distinct datasets. These datasets consist of a primary sample containing the outcome and a subset of the covariates, and a supplemental sample comprising information only on the full set of covariates. Previous methods have proposed doubly robust estimation procedures that employ a single propensity score model for the data fusion process and a single imputation model for the covariates available only in the supplemental dataset. However, it may be questionable to assume that either model is correctly specified due to an unknown data generating process. To address this issue, an empirical likelihood based approach that calibrates multiple propensity scores and imputation models is introduced. The resulting estimator is consistent when any one of the models is correctly specified and is robust against extreme values of the fitted propensity scores. The asymptotic normality property and the estimation efficiency are also discussed. Simulation studies show that the proposed estimator has substantial advantages over existing estimators, and an assembled U.S. household expenditure data example is used for illustration. [ABSTRACT FROM AUTHOR]

Abstract Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration. [ABSTRACT FROM AUTHOR]