Long-term sleep monitoring through the use of wearable EEG-based systems generates large volumes of data that need to be either locally stored or wireless transmitted. Compression of data can play a vital role to reduce the power consumption of these already resource-constrained systems. While compression methods can result in significantly reduced data storage and transmission requirements, the loss in signal information can have an impact on the algorithms used to extract the key sleep parameters. This paper studies the impact of six different state-of-the-art compression methods, including wavelet, SPIHT, filter and predictor-based methods, analysing their effects on the reconstructed signal quality particularly for automatic sleep staging applications. It looks at how the overall sleep staging accuracy as well as the detection accuracy of different sleep stages is reduced as a result of different EEG compression methods. It shows that the SPIHT and predictor-based compression methods outperform wavelet and filter-based methods in preserving the relevant signal features. It also shows that compression ratios of up to 65 can be achieved using the QSPIHT method with less than 10% loss in overall sleep staging accuracy. INDEX TERMS Sleep disorders, Electroencephalogram (EEG) compression, lossy compression, wearables, brain monitoring, sleep staging.