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Abstract:
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Recently, there has been an increased interest in combining probability and non-probability samples. Non-probability samples are cheaper and quicker to conduct. However, the resulting estimators are vulnerable to bias as the selection probabilities are unknown. To adjust for the potential bias, estimation procedures based on parametric or nonparametric models have been discussed in the literature. The validity of the resulting estimators depends on the validity of the underlying model. Nonparametric approaches may suffer from the curse of dimensionality and loss of efficiency. We propose a data integration approach by combining multiple outcome regression models and propensity score models. The proposed approach can be used for estimating general parameters including totals, means, distribution functions and percentiles. The resulting estimators are multiply robust in the sense that they remain consistent if all but one model are misspecified. The asymptotic properties of point and variance estimators are established. The results from a simulation study shows the benefits of the proposed method in terms of bias and efficiency.
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