Abstract

Non-probability samples are increasingly present in our daily lives; examples include online surveys, large-scale datasets (Big Data), or experimental data sources—such as social networks. This is due to the absence of a pre-established probabilistic sampling design before data collection. These types of samples allow rapid and convenient access to information of interest. However, lacking a rigorous sampling design, we cannot guarantee that the sample is representative, which can lead to biased estimates even when the sample size is large (Meng, 2018). Consequently, various techniques, depending on the available auxiliary information, have been developed to obtain more reliable and accurate estimates. Among the most studied and commonly used are Inverse Propensity Weighting, where the inclusion probabilities of the non-probability sample are estimated, and Mass Imputation, where the variable of interest is predicted —modeled from the non-probability sample— for a (usually smaller) reference sample probability from the same target population, for which such information is unknown.

Another prominent method in statistical practice is the Bootstrap method (Efron, 1979), widely used for variance estimation and to construct confidence intervals when analytical expressions are not ideally applicable. It can also be used to estimate the bias of an estimator, which would represent a major breakthrough in the context of non-probability sampling. Based on these and many other interesting applications, such as those presented in Arisido et al. (2021), we decided to explore the potential applications of the Bootstrap method in the context of non-probability samples. However, this context is particularly unique, as we use two samples for each estimator (the non-probability sample and the reference probability sample), a scenario not considered in the classical Bootstrap framework, and the sampling design of one of them is unknown—and likely not i.i.d. Some approaches have already been proposed in this context for estimating estimator variance (Kim et al., 2021; Rueda-Sánchez et al., 2026 [submitted]).

In this work, we explore the challenges and strengths of the Bootstrap method in the context of non-probability samples, and we examine a wide range of potential applications, including variance estimation, bias estimation, and others, through an extensive simulation study.