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Activity Number: 556
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract #321428
Title: Variable Selection and Direction Estimation for Single-Index Models via DC-TGDR Method
Author(s): Xi Liu* and Shuangge Ma and Wei Zhong
Companies: Xiamen University and Yale University and Xiamen University
Keywords: Single-index model ; Variable selection ; Distance covariance ; Threshold gradient directed regularization ; High-dimensional data
Abstract:

In this paper, we propose a new approach to select significant covariates and estimate the single-index direction simultaneously for single-index models. An efficient Threshold Gradient Directed Regularization (DC-TGDR) method is developed via maximizing Distance Covariance between the single index and the response variable. The resulting coefficient paths closely correspond to those induced by commonly used penalization methods. Its key feature is that we avoid estimating nonlinear link function of the single index. Compared with other methods, our method keeps model-free advantage from the view of sufficient dimension reduction and requires neither predictors nor response variable to be continuous. In addition, DC-TGDR method encourages grouping selection, which can keep the highly correlated covariates in or out of the model together. When the dimension of covariates is high and true model is sparse, DC-TGDR method maintains stability and efficiency due to its regularization property. We examine the finite sample performance of the newly proposed procedure by Monte Carlo simulation and a real data analysis.


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