In this paper, we investigate the resource allocation problem for the downlink non-orthogonal multiple access (NOMA) system with imperfect channel state information (CSI). We first derive closed-form expressions for the outage probabilities with and without the estimated instantaneous channel fading coefficient for each user. Upper bounds on both of the probability expressions above are proposed. Based on the outage probability bounds, we propose the power allocation scheme which is combined with a user selection step to minimize the maximum of the outage probability bounds of all the users. Simulation results show that the maximum outage probability can be significantly decreased by exploiting the priori knowledge of the estimated instantaneous channel fading coefficient for each user.