Nonparametric predictive pairwise comparison for real-valued data with terminated tails

This paper presents a statistical method for comparison of two groups of real-valued data, based on nonparametric predictive inference (NPI), with the tails of the data possibly terminated, leading to small values being left-censored and large values being right-censored. Such tails termination can occur due to several reasons, including limits of detection, consideration of outliers, and specific designs of experiments. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. We present NPI lower and upper probabilities for the event that the value of a future observation from one group is less than the value of a future observation from the other group, and we discuss several special cases that relate to well-known statistical problems.