The high efficiency video coding (HEVC) standard has highly improved the coding efficiency by adopting hierarchical structures of coding unit (CU), prediction unit (PU), and transform unit (TU). However, enormous computational complexity is introduced due to the recursive rate-distortion optimization (RDO) process on all CUs, PUs and TUs. In this paper, we propose a fast and efficient mode decision algorithm based on the Neyman-Pearson rule, which consists of early SKIP mode decision and fast CU size decision. First, the early mode decision is modeled as a binary classification problem of SKIP/non-SKIP or split/unsplit. The Neyman-Pearson-based rule is employed to balance the rate-distortion (RD) performance loss and the complexity reduction by minimizing the missed detection with a constrained incorrect decision rate. A nonparametric density estimation scheme is also developed to calculate the likelihood function of the statistical parameters. Furthermore, an online training scheme is employed to periodically update the probability density distributions for different quantization parameters (QPs) and CU depth levels. The experimental results show that the proposed overall algorithm can save 65% and 58% computational complexity on average with a 1.29% and 1.08% Bjontegaard Delta bitrate (BDBR) increase for various test sequences under random access and low delay P conditions, respectively. The proposed overall scheme also has the advantage that it can make the trade-off between the RD performance and time saving by setting different values for the incorrect decision rate.