Abstract: An effective processing and analysis of data streams is of utmost importance for a plethora of emerging applications like network monitoring, traffic management, and financial tickers. In addition to the management of transient and potentially unbounded streams, their analysis with advanced data mining techniques has been identified as a research challenge. A well-established class of mining techniques is based on nonparametric statistics where especially nonparametric density estimation is among the essential building blocks. In this paper, we examine the maintenance of nonparametric estimators over data streams. We present a tailored framework that incrementally maintains a nonparametric estimator over a data stream while consuming only a fixed amount of memory. Our framework is memory-adaptive and therefore, supports a fundamental requirement for an operator within a data stream management system. As an example, we apply our framework to selectivity estimation of range...