Quantile regression and variable selection for the single-index model |
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Authors: | Yazhao Lv Weihua Zhao Jicai Liu |
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Institution: | 1. Department of Statistics, East China Normal University, Shanghai 200241, People's Republic of China;2. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018, People's Republic of China;3. School of Science, NanTong University, NanTong 226007, People's Republic of China |
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Abstract: | In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set. |
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Keywords: | single-index model quantile regression variable selection adaptive LASSO oracle property |
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