Estimation of a discrete distribution function from a non-probability sample: an uncertainty based approach

Thomas M. Menino Convention & Exhibition Center 

In the latest decade, the relevance of non-probability samples is considerably increased because
of the decay of response rates in traditional sample surveys, and the availability of massive
datasets at a relatively low cost. In probability sampling, each unit of the population has
a known, non-zero probability of being selected. Non-probability samples involve, on the contrary,
uncontrolled methods for selecting of units into the sample. This implies that inclusion probabilities
are unknown, and then it is not possible, through the Inverse Probability Weighting principle, to
remove the selection bias. Furthermore, the unknown selection mechanism is frequently selective
with respect to the target population, so estimates of population characteristics may be subject to
serious selection bias. The basic question, therefore, is how to draw inference from such samples,
for population parameters of interest.
As a major effect of the uncontrolled selection mechanism, unless very restrictive assumptions are
made, the distribution of the character of interest is unidentifiable. 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 introduced. Furthermore, the reduction of uncertainty due to
the availability of extra-sample in formation is discussed.

informative sample

non-probability sample

uncertainty