The Detection, Identification, and Adaptation (DIA) estimator theoretical framework captures the combined parameter estimation and statistical hypothesis testing. For positioning problems in the context of safety-of-life applications (e.g., civil aviation, automated driving), accounting for the aforementioned combination is critical to ensure positioning safety. To gain further insights into the DIA estimator theoretical framework, we explore several aspects. We (i) compare the DIA framework with Advanced Receiver Autonomous Integrity Monitoring (ARAIM), (ii) compute the integrity risk and upper bounds for it, (iii) evaluate the probability of distancing failure based on the distance between two DIA estimators, and (iv) investigate the problem of hypotheses detectability and identifiability. All these aspects are covered in the context of a simple two-dimensional user range-based positioning problem using four radio transmitters at known locations.