Mark-recapture techniques in statistical tests for imprecise data

We aim to construct suitable tests when we have imprecise information about a sample. More specifically, we assume that we get a collection of n sets of values, each one characterizing an imprecise measurement. Each set specifies where the true sample value is (and where it is not) with full confidence, but it does not provide any additional information. Our main objectives are twofold: first we will review different kinds of tests in the literature about inferential statistics with random sets and discuss the approach that best suits our definition of imprecise data. Secondly, we will show that we can take advantage from mark and recapture techniques to improve the accuracy of our decisions. These techniques will be specially important when the population is small enough (with respect to the sample size) that recaptures are common. They also seem to be useful when resampling techniques are involved in the decision process.