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In this paper, the ergodic sum rate maximization problem is considered in the multiple-input single-output non-orthogonal multiple access (NOMA) system with statistical channel state information at the transmitter. First, we derive the analytic expression of the ergodic sum rate with given arbitrary precoders. Then, due to the non-convexity of the optimization problem, we use the gradient projection algorithm (GPA) to find the optimal precoders, approximately. In extremely low and extremely high signal-to-noise ratio (SNR) region, we deduce the closed-form optimal precoders and a simplified analytic expression of the ergodic sum rate, based on which another algorithm leveraging bisection algorithm (BA) is proposed in the arbitrary-SNR. Numerical results demonstrate that the GPA and BA can efficiently find the optimal precoding vectors, approximately, and the performance of NOMA is superior to the orthogonal multiple access and space division multiple access in intermediate- and high-SNR.