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Quantile Estimation and Variable Selection of Partially Linear Single-index Models

Yiqiang Lu, Feng Li, Bin Hu

Abstract



Partially linear single-index model is one of the most popular semiparametric models. In this paper, we present an overall treatment of parametric estimation and variable selection of partially linear single-index quantile (PLSIQ) regression. PLSIQ model is estimated by minimizing the average loss function. Based on the minimized average loss estimation (MALE), the variable selection is done by minimizing the average loss with adaptive l1 penalty. Under some mild conditions, we demonstrate the asymptotic properties of MALE and the oracle properties of adaptive LASSO procedure for PLSIQ model. Some simulations are done to illustrate the performance of the proposed methods.

Keywords


partially linear single-index model, quantile regression, adaptive LASSO, vari- able selection

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