Estimation of the distribution function and quantiles through data integration

Abstract

collecting detailed data from individuals. Non-probability sampling is a relatively inexpensive data source, although they require special treatment because the estimate may suffer from sample selection bias. In this paper, we consider methods for integrating a non-representative volunteer sample into a probability survey. We investigate several approaches to correcting non-probability sample selection bias in the estimation of the distribution function. We combine the estimators of the distribution function that correct the selection bias with the design unbiased estimators based on the probability sample. Our methodology for combining the voluntary and probability samples can be applied to other non-linear parameters. Empirical evidence of the improvements offered by the proposed methodology is provided in simulation settings.