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We consider a two-way amplify-and-forward (AF) relaying system consisting of two source nodes and a half-duplex relay. We assume that the source nodes are equipped with the linear minimum mean squared error (LMMSE) channel estimators. We investigate the effect of uncertainty due to channel estimation error on the system outage probability, considering the imposed bandwidth and energy costs of channel estimation. For a fixed transmission block length and a total transmit power constraint, we provide a compact-form expression for the system outage probability upper bound and we explore the optimal number of training symbols, the optimal power allocation between data and training, and the optimal power allotment between the two users and the relay, such that this bound is minimized. Our numerical results show that channel estimation error does not limit the performance in high signal-to-noise ratio (SNR). Also, the optimal power allocation between data and training and between the users and the relay provides a significant SNR improvement, compared with the suboptimal schemes, including fixed power allocation. The optimization gain increases as the relay moves away from the middle point.