Real-time video analytics on the edge is challenging as the computationally constrained resources typically cannot analyse video streams at full fidelity and frame rate, which results in loss of accuracy. This paper proposes a Transprecise Object Detector (TOD) which maximises the real-time object detection accuracy on an edge device by selecting an appropriate Deep Neural Network (DNN) on the fly with negligible computational overhead. TOD makes two key contributions over the state of the art: (1) TOD leverages characteristics of the video stream such as object size and speed of movement to identify networks with high prediction accuracy for the current frames; (2) it selects the best-performing network based on projected accuracy and computational demand using an effective and low-overhead decision mechanism. Experimental evaluation on a Jetson Nano demonstrates that TOD improves the average object detection precision by 34.7 % over the YOLOv4-tiny-288 model on average over the MOT17Det dataset. In the MOT17-05 test dataset, TOD utilises only 45.1 % of GPU resource and 62.7 % of the GPU board power without losing accuracy, compared to YOLOv4-416 model. We expect that TOD will maximise the application of edge devices to real-time object detection, since TOD maximises real-time object detection accuracy given edge devices according to dynamic input features without increasing inference latency in practice.