Penalized least squares for single index models |
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Authors: | Heng Peng Tao Huang |
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Institution: | 1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;2. Department of Statistics, University of Virginia, Charlottesville, VA 22904, United States |
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Abstract: | The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squares method to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously. When the dimension of parameters in the single index model is a fixed constant, under some regularity conditions, we demonstrate that the proposed estimators for parameters have the so-called oracle property, and furthermore we establish the asymptotic normality and develop a sandwich formula to estimate the standard deviations of the proposed estimators. Simulation studies and a real data analysis are presented to illustrate the proposed methods. |
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