High Definition (HD) maps have become core supporting components for autonomous driving. To date, their updates heavily depend on the vehicle fleets of the map vendors, which cannot scale and timely reflect the highly dynamic environment. To ensure the HD map quality, it is advocated social vehicles should be used. Nevertheless, there are privacy concerns and a lack of incentives for social vehicles to contribute data. In this paper, we leverage federated analytics (FA), a newly developed collaborative data analytics paradigm, where raw data are kept local and only the insights generated from local analytics are sent to a server for aggregation. We present a new Federated Analytics based HD map Updating model (FAUMap) to protect the privacy of social vehicles. To motivate social vehicles to contribute data and improve the HD map quality, we formulate an overlapping coalition formation game, OCFUMap, and develop an algorithm to find feasible coalitions. Simulations show that our approach can improve the quality of the updated HD map by 1.56 times. To study an end-to-end operation of the FAUMap model and OCFUMap game, we present a case of HD map updates of the Powell street in San Francisco using the autonomous driving simulator CarLA.