Dynamic spectrum access has been proposed as a means to share scarce radio resources, and requires devices to follow protocols that access spectrum resources in a proper, disciplined manner. For a cognitive radio network to achieve this goal, spectrum policies and the ability to enforce them are necessary. Detection of an unauthorized (anomalous) usage is one of the critical issues in spectrum etiquette enforcement. In this paper, we present a network structure for dynamic spectrum access and formulate the anomalous usage detection problem using statistical significance testing. The detection problem investigated considers two cases, namely, the authorized (primary) transmitter is (i) mobile and (ii) fixed. We propose a detection scheme for each case by exploiting the spatial pattern of received signal energy across a network of sensors. Analytical models are formulated when the distribution of the energy measurements is given and, due to the intractability of the general problem, we present an algorithm using machine learning techniques to solve the general case when the statistics of the energy measurements are unknown. Our simulation results show that our approaches can effectively detect unauthorized spectrum usage with a detection probability above 0.9 while keeping the false alarm rate less than 0.1 when only one unauthorized radio is present, and the detection probability is even higher for more unauthorized radios.