In cognitive radio network, wideband spectrum sensing is faced with the technical restrictions of high-speed Analog-to-Digital Converter (ADC). To cope with this issue, the probability distribution of high-order decision statistics for wideband spectrum sensing fed by compressed observations based on Compressive Sampling (CS) theory was deduced, and then a High-Order Statistics (HOS)-based Compressive Wideband Spectrum Blind Detection (HOS-CWSBD) scheme with theses compressive measurements was proposed in this paper. The proposed algorithm need neither the prior acknowledge of the transmitted signal, nor the signal recovery. Both theoretical analyses and simulation results show that the proposed scheme has lower computational complexity and more robustness to the noise uncertainty compared to the traditional spectrum sensing schemes based on CS requiring the signal recovery and the HOS-based spectrum sensing scheme with Nyquist samples.