Dynamic spectrum access has been proposed as a means to share scarce radio resources, and requires devices to follow protocols that use 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 is classified into two subproblems. For the case where no authorized signal is present, we describe the existing cooperative sensing schemes and investigate the impact of signal path loss on their performance. For the case where an authorized signal is present, we propose three methods that detect anomalous transmissions by making use of the characteristics of radio propagation. Analytical models are formulated for two special cases and, due to the intractability of the general problem, we present an algorithm using machine learning techniques to solve the general case. Our simulation results show that our approaches can effectively detect unauthorized spectrum usage with high detection rate and low false positive rate.