This letter studies the multiple-input single-output (MISO) non-orthogonal multiple-access (NOMA) downlink using regularized zero-forcing (RZF) precoding with imperfect channel state information (CSI). We first propose a new user scheduling scheme based on imperfect CSI and a model to characterize the channel correlation between the weak and strong users. Then we derive an approximate expression of the ergodic sum-rate using large-system random matrix theory. This approximation permits us to derive the optimal power allocation scheme that satisfies the rate requirement of the weak users. Simulation results are presented to confirm the accuracy of the approximation and reveal the relationships between the ergodic sum-rate, the channel correlation, and other system parameters.