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Nonline-of-sight (NLOS) propagation is one of the challenges in radio positioning. Significant attention has been drawn to the mitigation of the NLOS effect in recent years. This paper focuses on the identification of NLOS conditions by employing the statistical decision theory. A Neyman-Pearson (NP) test method is first derived for scenarios where either 1-D or 2-D angular measurements are provided. A time-of-arrival (TOA) based method is then developed under idealized conditions to provide a performance reference. In the presence of both TOA and received signal strength (RSS) measurements, a joint identification method is derived to efficiently exploit the TOA and RSS measurements. Analytical expressions of the probability of detection (POD) and the probability of false alarm (PFA) are derived for all the scenarios considered. Two theorems and one corollary regarding the line-of-sight (LOS) conditions based on the angle of arrival (AOA) are also presented, and the proofs are provided. Simulation results demonstrate that the proposed methods perform well, and the joint TOA- and RSS-based method considerably outperforms the TOA-based methods. The proposed methods are robust to the model errors, as demonstrated through simulations. It is also shown that the analytical results agree well with the simulated ones.