Approximate query processing (AQP) has gained traction as an effective technique for executing queries on big data. Bounded approximate query processing (BAQ) is a recently proposed framework that stores a summary of an original table as a synopsis and ensures that its approximation errors remain below a user-specified threshold. Based on the BAQ framework, we proposed BAQ± to shrink a synopsis and improve query processing speed while guaranteeing strict error bounds. However, BAQ and BAQ± still have limitations in constructing synopses. They require time-consuming data sorting for each numerical attribute and cannot summarize high-cardinality categorical attributes, such as spatiotemporal data. To overcome these problems, we propose a novel framework called Hierarchical BAQ (HBAQ) and a synopsis construction method in this paper. HBAQ constructs multiple synopses based on the dimension tables of several categorical attributes and uses them to answer OLAP queries efficiently. We also introduce a new bucket definition to summarize numerical attributes effectively and support incremental updates for synopses. The experimental results show that HBAQ achieves half the construction time of BAQ with lower memory consumption. Furthermore, HBAQ can answer OLAP queries more efficiently than BAQ while ensuring strictly bounded errors.