Combined-penalized likelihood estimations with a diverging number of parameters |
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Authors: | Ying Dong Lixin Song Ying Xu |
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Affiliation: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, People's Republic of China;2. Faculty of Science, Dalian Nationalities University, Dalian 116600, People's Republic of China |
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Abstract: | In the economics and biological gene expression study area where a large number of variables will be involved, even when the predictors are independent, as long as the dimension is high, the maximum sample correlation can be large. Variable selection is a fundamental method to deal with such models. The ridge regression performs well when the predictors are highly correlated and some nonconcave penalized thresholding estimators enjoy the nice oracle property. In order to provide a satisfactory solution to the collinearity problem, in this paper we report the combined-penalization (CP) mixed by the nonconcave penalty and ridge, with a diverging number of parameters. It is observed that the CP estimator with a diverging number of parameters can correctly select covariates with nonzero coefficients and can estimate parameters simultaneously in the presence of multicollinearity. Simulation studies and a real data example demonstrate the well performance of the proposed method. |
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Keywords: | asymptotic normality Bayesian information criterion combined-penalization oracle property variable selection |
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