Similarity based one-sided tests for the expected value and interval data

A novel way for addressing one-sided hypothesis tests for the mean of unable to observe real random variables from which we have information provided in terms of interval data is proposed. For this purpose, a measure of similarity between intervals is considered and the classical one-sided hypothesis test to check whether the similarity between the expectation of a random interval and a subset of an specific unbounded interval is high enough. Asymptotic and bootstrap techniques are applied in order to study the limit distribution of the proposed test statistic. Some simulations have been carried out in order to show the empirical behavior of the test.