Unsupervised anomaly detection plays a crucial role in many critical applications. Driven by the success of deep learning, recent years have witnessed growing interests in applying deep neural networks (DNNs) to anomaly detection problems. A common approach is using autoencoders to learn a feature representation for the normal observations in the data. The reconstruction error of the autoencoder is then used as outlier scores to detect the anomalies. However, due to the high complexity brought upon by the over-parameterization of DNNs, the reconstruction error of the anomalies could also be small, which hampers the effectiveness of these methods. To alleviate this problem, we propose a robust framework using collaborative autoencoders to jointly identify normal observations from the data while learning its feature representation. We investigate the theoretical properties of the framework and empirically show its outstanding performance as compared to other DNN-based methods. Our experimental results also show the resiliency of the framework to missing values compared to other baseline methods.