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A Piecewise Single-Index Model for Dimension Reduction

In this article we propose to use different single-index models for observations in different regions of the sample space. This approach inherits the estimation efficiency of the single-index model in each region, and at the same time allows the global model to have multidimensionality in the sense of conventional dimension reduction. On the other hand, the model can be seen as an extension of CART and a piecewise linear model proposed. Modeling procedures, including identifying the region for every single-index model and estimation of the single-index models, are developed. Simulation studies and real data analysis are employed to demonstrate the usefulness of the approach. Computer code and technical details of the method are provided as supplementary material online.