Pretest estimation in combining probability and non-probability samples

Multiple heterogeneous data sources are becoming increasingly available for statistical analyses in the era of big data. As an important example finite-population inference, we develop a unified framework test-and-pool approach to general parameter estimation by combining gold-standard probability and non-probability samples. We focus on case when study variable is observed both datasets estimating target parameters, each contains other auxiliary variables. Utilizing design, conduct pretest procedure determine comparability with decide whether or not leverage pooled analysis. When comparable, our combines efficient estimation. Otherwise, retain only also characterize asymptotic distribution proposed estimator under local alternative provide data-adaptive select critical tuning parameters that smallest mean square error estimator. Lastly, deal non-regularity estimator, construct robust confidence interval has good finite-sample coverage property.