The robotics community continually strives to create robots that are deployable in real-world environments. Often, robots are expected to interact with human groups. To achieve this goal, we introduce a new method, the Robot-Centric Group Estimation Model (RoboGEM), which enables robots to detect groups of people. Much of the work reported in the literature focuses on dyadic interactions, leaving a gap in our understanding of how to build robots that can effectively team with larger groups of people. Moreover, many current methods rely on exocentric vision, where cameras and sensors are placed externally in the environment, rather than onboard the robot. Consequently, these methods are impractical for robots in unstructured, human-centric environments, which are novel and unpredictable. Furthermore, the majority of work on group perception is supervised, which can inhibit performance in real-world settings. RoboGEM addresses these gaps by being able to predict social groups solely from an egocentric perspective using RGB-D data. To achieve group predictions, RoboGEM leverages joint motion and proximity estimations. We evaluated RoboGEM against a challenging, egocentric, real-world dataset where both pedestrians and the robot are in motion simultaneously, and show RoboGEM outperformed two state-of-the-art supervised methods in detection accuracy by up to 30%, with a lower miss rate. Our work will be helpful to the robotics community, and serve as a milestone to building unsupervised systems that will enable robots to work with human groups in real-world environments.