An Uncertainty Based Approach for Dealing With Selection Bias in Non-Probability Samples

The main issue with non-probability samples is that the standard design-based approach cannot be applied as the selection mechanism is unknown. In this paper, the concept of uncertainty on data generating model, resulting from the lack of knowledge of the sampling design acting in the non-probability sample, is discussed. Furthermore, the effect on uncertainty due to the availability of extra-sample information is evaluated. First of all, the class of plausible distributions for the variable of interest is defined, a measure of uncertainty is introduced and its asymptotic properties are analysed. Next, a plausible estimate of the distribution of the variable of interest is constructed and its accuracy is evaluated. Finally, a simulation study is performed, and an application to a real case is provided.