Estimation and variable selection for generalised partially linear single-index models |
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Authors: | Peng Lai Ye Tian |
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Institution: | 1. School of Mathematics and Statistics, Nanjing University of Information Science &2. Technology, Nanjing 210044, People's Republic of China;3. Division of Mathematical Sciences, SPMS, Nanyang Technological University, Singapore 637371, Singapore |
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Abstract: | In this paper, we study the problem of estimation and variable selection for generalised partially linear single-index models based on quasi-likelihood, extending existing studies on variable selection for partially linear single-index models to binary and count responses. To take into account the unit norm constraint of the index parameter, we use the ‘delete-one-component’ approach. The asymptotic normality of the estimates is demonstrated. Furthermore, the smoothly clipped absolute deviation penalty is added for variable selection of parameters both in the nonparametric part and the parametric part, and the oracle property of the variable selection procedure is shown. Finally, some simulation studies are carried out to illustrate the finite sample performance. |
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Keywords: | oracle property quasi-likelihood SCAD penalty variable selection |
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