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A new technique, called statistical neuro-space mapping, is proposed for large-signal statistical modeling of nonlinear microwave devices. The proposed technique is an advance over a recent linear statistical mapping technique. It uses nonlinear mapping to overcome the accuracy limitations of the linear mapping in modeling large statistical variations among different devices. For a given population of device samples, the nominal device model is determined from dc, small-, and large-signal data. The behavior of a random device in the population is obtained by a nonlinear mapping from that of the nominal device. The unknown mapping function is represented by neural networks trained using dc and small-signal data of various devices in the population. A novel statistical mapping is formulated by introducing a compact set of statistical variables to control the mapping to map from the nominal device toward different devices in the population. A new training method is proposed for simultaneous statistical parameter extraction and neural-network training. The proposed technique is confirmed by statistical modeling of microwave transistor examples, and use of the models in statistical analyses of a two-stage amplifier. It is demonstrated that, for small or large statistical variations, the proposed technique outperforms the existing methods, using a minimum amount of expensive large-signal data to provide the most accurate large-signal statistical model.