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The statistical challenges in using big data for making valid statisticalinference in the finite population have been well documented in literature.These challenges are due primarily to statistical bias arising fromunder-coverage in the big data source to represent the population of interestand measurement errors in the variables available in the data set. Bystratifying the population into a big data stratum and a missing data stratum,we can estimate the missing data stratum by using a fully respondingprobability sample, and hence the population as a whole by using a dataintegration estimator. By expressing the data integration estimator as aregression estimator, we can handle measurement errors in the variables in bigdata and also in the probability sample. We also propose a fully nonparametricclassification method for identifying the overlapping units and develop abias-corrected data integration estimator under misclassification errors.Finally, we develop a two-step regression data integration estimator to dealwith measurement errors in the probability sample. An advantage of the approachadvocated in this paper is that we do not have to make unrealisticmissing-at-random assumptions for the methods to work. The proposed method isapplied to the real data example using 2015-16 Australian Agricultural Censusdata.

Data Integration by combining big data and survey sample data for finite population inference