Abstract

Data from the non-probability and probability samples are combined to estimate finite population total. Assuming the values of the study variable are available in both samples, under independence of the pseudo-inclusion indicators to the non-probability sample, the integration of the non-probability sample and probability sample through the composite estimator of the population total is studied. The integration is composed of the linear combination of the inverse probability weighted (IPW) estimator and a traditional design-based estimator. Evaluating the variance of the former estimator, the randomness of the underlying non-probability sample is taken into account through the distribution of the estimated propensity scores. Non-sampling errors are not taken into account. This approach is compared with an estimator obtained by other authors and with a bootstrap variance estimator. The proposed linear combination is robust to the miss-specification of the model for the propensity scores due to incorporated estimator of bias of the IPW estimator. The number of Lithuanian companies possessing the websites is estimated in the simulation study. By combining the sample survey data and the big voluntary sample data, the properties of the introduced estimators are demonstrated.