In this paper, we propose a new framework for anomaly detection in medical wireless sensor networks, which are used for remote monitoring of patient vital signs. The proposed framework performs sequential data analysis on a mini gateway used as a base station to detect abnormal changes and to cope with unreliable measurements in collected data without prior knowledge of anomalous events or normal data patterns. The proposed approach is based on the Mahalanobis distance for spatial analysis, and a kernel density estimator for the identification of abnormal temporal patterns. Our main objective is to distinguish between faulty measurements and clinical emergencies in order to reduce false alarms triggered by faulty measurements or ill-behaved sensors. Our experimental results on both real and synthetic medical datasets show that the proposed approach can achieve good detection accuracy with a low false alarm rate (less than 5.5%).