QR Prediction for Statistical Data Integration

In this paper, we investigate how a big non-probability database can be used to improve estimates from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more eÿcient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, proposed by Särndal and Wright (1984) to handle the case where the non-probability database contains auxiliary variables but no study variable. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. Assuming the probability sampling design is not informative, the QR predictor is also model-unbiased regardless of the validity of those conditions. We compare the design properties of di˙erent predictors, in the class of QR predictors, through a simulation study. They include a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. As expected, the model-based predictor did not perform well when the underlying model was misspecified.