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We consider monitoring the quality of compressed video transmitted over a packet network from the perspective of a network service provider. Our focus is on no-reference methods, which do not access the original signal, and on evaluating the impact of packet losses on quality. We present three methods to estimate mean squared error (MSE) due to packet losses directly from the video bitstream. NoParse uses only network-level measurements (like packet loss rate), QuickParse extracts the spatio-temporal extent of the impact of the loss, and FullParse extracts sequence-specific information including spatio-temporal activity and the effects of error propagation. Our simulation results with MPEG-2 video subjected to transport packet losses illustrate the performance possible using the three methods.