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We present EgoRenderer, a system for rendering full-body neural avatars of a person captured by a wearable, egocentric fisheye camera that is mounted on a cap or a VR headset. Our system renders photorealistic novel views of the actor and her motion from arbitrary virtual camera locations. Rendering full-body avatars from such egocentric images come with unique challenges due to the top-down view and large distortions. We tackle these challenges by decomposing the rendering process into several steps, including texture synthesis, pose construction, and neural image translation. For texture synthesis, we propose Ego-DPNet, a neural network that infers dense correspondences between the input fisheye images and an underlying parametric body model, and to extract textures from egocentric inputs. In addition, to encode dynamic appearances, our approach also learns an implicit texture stack that captures detailed appearance variation across poses and viewpoints. For correct pose generation, we first estimate body pose from the egocentric view using a parametric model. We then synthesize an external free-viewpoint pose image by projecting the parametric model to the user-specified target viewpoint. We next combine the target pose image and the textures into a combined feature image, which is transformed into the output color image using a neural image translation network. Experimental evaluations show that EgoRenderer is capable of generating realistic free-viewpoint avatars of a person wearing an egocentric camera. Comparisons to several baselines demonstrate the advantages of our approach.