Epidemic transitions are an important feature of infectious disease systems. As the transmissibility of a pathogen increases, the dynamics of disease spread shifts from limited stuttering chains of transmission to potentially large scale outbreaks. One proposed method to anticipate this transition are early-warning signals (EWS), summary statistics which undergo characteristic changes as the transition is approached. Although theoretically predicted, their mathematical basis does not take into account the nature of epidemiological data, which are typically aggregated into periodic case reports and subject to reporting error. The viability of EWS for epidemic transitions therefore remains uncertain. Here we demonstrate that most EWS can predict emergence even when calculated from imperfect data. We quantify performance using the area under the curve (AUC) statistic, a measure of how well an EWS distinguishes between numerical simulations of an emerging disease and one which is stationary. Values of the AUC statistic are compared across a range of different reporting scenarios. We find that different EWS respond to imperfect data differently. The mean, variance and first differenced variance all perform well unless reporting error is highly overdispersed. The autocorrelation, autocovariance and decay time perform well provided that the aggregation period of the data is larger than the serial interval and reporting error is not highly overdispersed. The coefficient of variation, skewness and kurtosis are found to be unreliable indicators of emergence. Overall, we find that seven of ten EWS considered perform well for most realistic reporting scenarios. We conclude that imperfect epidemiological data is not a barrier to using EWS for many potentially emerging diseases.