In this paper, we present an efficient method for radio frequency interference (RFI) detection based on cyclic spectrum analysis that relies on compressive statistical sensing to estimate the cyclic spectrum from sub-Nyquist data. We refer to this method as compressive statistical sensing (CSS), since we utilize the statistical autocovariance matrix from the compressed data. We demonstrate the performance of this algorithm by analyzing radio astronomy data acquired from the Arecibo Observatory (AO)'s L-Wide band receiver (~1.3 GHz), which is typically corrupted by active radars for commercial applications located near AO facilities. Our CSS-based solution enables robust and efficient detection of the RFI frequency bands present in the data, which is measured by receiver operating characteristic (ROC) curves. As a result, it allows fast and computationally efficient identification of RFI-free frequency regions in wideband radio astronomy observations.