Inclusion degree tests for the Aumann expectation of a random interval

An extension of the inclusion test of the expected value of a real random variable in an interval to the case of general random intervals is introduced. The hypothesis of strict inclusion is relaxed by considering a measure of the degree of inclusion. Thus, partial inclusions are also tested. Asymptotic and bootstrap techniques are established. The performance of the bootstrap test is also analyzed by means of some simulations. A case-study regarding the blood pressure classification in adults is considered.