Abstract:
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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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