Simultaneous Location and Mapping (SLAM) is a key problem to solve in order to build truly autonomous mobile robots. SLAM with a unique camera, or monocular SLAM, is probably one of the most complex SLAM variants, based entirely on a bearing-only sensor working over six DOF. The monocular SLAM method developed in this work is based on the Delayed Inverse-Depth (DI-D) Feature Initialization, with the contribution of a new data association batch validation technique, the Highest Order Hypothesis Compatibility Test, HOHCT. The Delayed Inverse-Depth technique is used to initialize new features in the system and defines a single hypothesis for the initial depth of features with the use of a stochastic technique of triangulation. The introduced HOHCT method is based on the evaluation of statistically compatible hypotheses and a search algorithm designed to exploit the strengths of the Delayed Inverse-Depth technique to achieve good performance results. This work presents the HOHCT with a detailed formulation of the monocular DI-D SLAM problem. The performance of the proposed HOHCT is validated with experimental results, in both in door and outdoor environments, while its costs are compared with other popular approaches.