  Non-probability sampling, for example in the form of online panels, has
become a fast and cheap method to collect data. While reliable inference tools
are available for classical probability samples, non-probability samples can
yield strongly biased estimates since the selection mechanism is typically
unknown. We propose a general method how to improve statistical inference when
in addition to a probability sample data from other sources, which have to be
considered non-probability samples, are available. The method uses specifically
tailored regression residuals to enlarge the original data set by including
observations from other sources that can be considered as stemming from the
target population. Measures of accuracy of estimates are obtained by adapted
bootstrap techniques. It is demonstrated that the method can improve estimates
in a wide range of scenarios. For illustrative purposes, the proposed method is
applied to two data sets.
