An established method to detect concept drift in data streams is to perform statistical hypothesis testing on the multivariate data in the stream. Statistical decision theory offers rank-based statistics for this task. However, these statistics depend on a fixed set of characteristics of the underlying distribution. Thus, they work well whenever the change in the underlying distribution affects these properties measured by the statistic, but they perform not very well, if the drift influences the characteristics caught by the test statistic only to a small degree. To address this problem, we present three novel drift detection tests, whose test statistics are dynamically adapted to match the actual data at hand. The first one is based on a rank statistic on density estimates for a binary representation of the data, the second compares average margins of a linear classifier induced by the 1-norm support vector machine (SVM), and the last one is based on the average zero-one or si...