Radio-frequency identification (RFID) technologies have been widely used in many applications. Tag estimation, which is to estimate the cardinality of a single tag set, is an important research topic. This paper expands the estimation research as follows: It performs joint estimation between two tag sets, and more importantly the estimation is fine-grained in an effort to accommodate common practical scenarios, where each tag set consists of tags belonging to different categories. For any two given tag sets, we want to know the detailed information about the joint property of each category, instead of just the aggregate information of the whole sets. Furthermore, due to the open nature of RFID communications, it is often desirable that category-level joint estimation can be performed in an anonymous way without revealing the tags' IDs. To support these requirements, we develop a new technique called mask bitmap that can encode a tag set without requiring the tags to report their IDs or category IDs. Any two mask bitmaps that encode different tag sets can be combined to perform category-level joint estimation. Simulation results confirm that the proposed solution can yield accurate category-level estimates and preserve tags' anonymity.